All right, anything I say should be taken as "I want to help you" and not "I dislike you".
As long as that is understood, I'm willing to give you some decent critique. =]
Let's start by saying that you have an idea down, but you've a lot of work ahead of you, if you're willing to give it a chance to expand and grow into something you can be proud of.
Unfortunately, it is just an idea at this point. I say that because almost the entire premise of the story is summed up in two paragraphs and a sentence.

So flesh it out a bit, add some more facts in there that describe this world your character lives in. Give us more information, without simply giving us the entire plot right off the bat. =]
Now for some more commenting... =D
Your first sentence starts as if you are writing a children's fiction. You might as well have said "once upon a time".
My suggestion would be to
not introduce the story in this manner; though it is possible to use that line and actually introduce a story quite well.
Here are some examples of how you can start a story without falling into a cliché version of children's fiction.
More importantly, the first sentence should be one that brings us into the story, more than introducing the idea of the story (though it should encompass both, depending on the story - and in this case it should).
Your second sentence gives us an idea as to this character's lifestyle. He's all alone and rejected for doing something that he feels was right. This is a good starter sentence, actually, though it is missing some crucial information such as:
Did his family reject him, or are they dead? Tell the reader why they rejected him in specific. Don't have us guess that everyone suddenly decided to reject this boy due to his being a saviour to a chimera.
Did he have friends at his own age? If so, why wouldn't they help their friend instead of rejecting him? Tell us why.
Is it possible he's a runaway now? Living off the land?
Tell us why these people (past friends, family, etc.) haven't given information to the authorities to have the main character imprisoned, etc.
Further, how did he actually perform this rescue? He's 13, and apparently he "rescued" the beast from a "mystic" hunter. If I'm correct in assuming, I'd say that a mystic hunter is likely an experience chap with a few years under his belt, yes? How does he fail to capture/kill this chimera in time to prevent its rescue from the boy? Need I remind you, the boy is 13, and unless he is a prodigy of vast proportions, he really can't stop a grown man, and a mystic hunter no less, from having his way with a chimera (which is likely too much of a burden for the boy to carry and escape with, thus I'm assuming the chimera escaped on his own feet, which doesn't make the boy his rescuer).
This is all conjecture based on what you've written thus far, and you'll need to answer questions like these if you plan on maintaining the attention of a reader. =]
On another note, you mention that the reason that the boy is rejected by all who knew him, was solely based on the fact that he rescued the chimera (not that he cares about the chimera, or keeps him, or is breaking the law, etc.), and that's something you need to make more clear or reword, etc. ^^
Lastly, in relation to the second sentence, you need to tell the audience how the boy ended up knowing where to find the chimera in order to rescue him. Was the boy wandering around in a location where hunters hunt? (Unsafe and unlikely a decent excuse to put the situation in this area, so I'll assume not.) Was the boy already knowledgeable about the chimera and the hunter discovered the boy hiding the chimera in a cave somewhere local? (I doubt this, as it appears that the reason the chimera and the boy are friends is because the boy rescued the chimera, so I'll assume this isn't the case either.) Would it be then, that the hunter was chasing the chimera and the chimera happened upon a village where the boy resided and the boy discovered the chimera in pain and pitied the chimera? This would make the most sense, actually, though I'd have to be convinced that you somehow manage to tell the story in a way where the authorities weren't involved (as they'd know if a hunter was chasing a chimera through a village, methinks).
Just some food for thought there.

Your third sentence simply mentions a law, quoting the law, and based on its structure it should belong to the second sentence (add on using a semicolon). At any rate, I'll continue to discuss this sentence as if it were its own. =]
Whose law is this? Who does it govern? Why was it made? Are there examples of individuals who have violated this law? Does it apply to all age groups?
Also, you should not use past-tense in a quote like that. Primarily because all laws are written as present-tense, but also because this is no longer a direct quote from the law at this point; it's a summation of it.
I would recommend either removing it as a quote, or actually creating a law as it would be written. For example:
"By Imperial decree, any man, woman, or child in possession of a mystical beast, or found aiding a mystical beast, will be subject to inception into the Imperial Army. If the accused is unable or unwilling to serve in the Imperial Army, they will be put to death."Your fourth sentence is a bit confusing. Does the boy want to keep the chimera as a pet or as a collector's item? By mentioning its rarity, you can confuse the reader into believing that the chimera is more of a "bragging rights" tool than a "friend". But as we already know, owning this chimera is really not something to brag about. You also mentioned that the boy isn't interested in becoming a "major" part of the army. Are we then to assume that the boy is interested in becoming a part of the army, but only in a minor way?
Perhaps it would be better to say that the boy has no interest in becoming a part of the army based on the current terms of recruitment; if he has any interest at all.
So, let's start by saying that it is a good time to introduce the character's name (you did this), but perhaps not in the same sentence as the rest. I'd say that the fourth sentence could be turned into three separate sentences, each with their own idea. One introducing the character as Tomas, the 13-year old boy, one making mention that he does, or does not, have interest in becoming a part of the army, but he wants to maintain his friendship and activities with the chimera, and one expressing the rarity of owning a chimera as a pet.
Each of these topics can have their own paragraph, truly, and I'd recommend introducing each of these topics in a way that you can organise them properly according to the story as well as giving the reader enough information to go on.
If there is no significance to mentioning the chimera is a rarity, then I'd avoid mentioning it. Especially since "bragging rights" and/or "pride" are not valid points to be made in a story like this. (At least not until it is actually something that the boy is admired for, or becomes prideful of.)
On to the second paragraph... =D
Your first sentence here mentions a law, but we don't have a quote this time. So you'll need to determine whether or not you will be consistent in quoting laws, or if you'd prefer to just refer to them without the reader knowing what they actually say. I'd recommend having a written law, and quoting only the bits that are relative to the story - and not referring to any bits that aren't quoted in the story.
Also, do not begin a sentence "in all honesty" as you do not want the reader to assume at any point that you aren't being completely honest with them. A better phrase to use would be: "It was clear that". So it would read: "It was clear that the law said..."; this could also be said as: "The law clearly states...", and then quote the written law.
Fortunately the law you've made for the story makes sense, as you probably don't want anyone serving in the military at ages younger than 16. This is a good law to have, and based on the fact that your character is 13 (you need to mention this before mentioning the law, and I'd suggest you add it in there where you introduce the character by name), I'd make no direct argument to having him be unable to join the army at this point in the story. You do hint to the idea that it is a possibility though, despite the law mentioning that it is forbidden.
I don't understand why any information relative to becoming an officer is necessary at this point, so I think it would be best to remove that bit for now. Perhaps save the idea for later in the story, when and if it matters at all. Unless, of course, you are trying to imply that being an officer is possible at his young age. In which case, it would make more sense, but you need to be more clear for the reader's sake. =]
Whilst you probably don't want to spoon-feed every bit of information to the reader, you also don't want to frustrate them by mentioning something that seemingly doesn't have any relevance to anything (and if you do mention something in this manner, give a hint that it will be explained later on in the story - and don't forget to explain it later on in the story).

(Note that you used "in all honesty" and "to be honest" in the same sentence, and you should avoid doing this in the future.) ^^
Your second sentence basically tells the reader that the boy is a typical teenager who has a tendency to be rebellious toward authority. You could probably say it in many other ways, and probably should. I would say that you should use examples as to why he wants to be rebellious, in particular, and not just use the excuse of his age. A reader already is going to assume this about the boy's personality, but a reader is also very interested in knowing the "why and how" in relation to the boy's thoughts about him being rebellious (even if the boy doesn't recognise this trait about himself). As a reader, I'd like to know why he wants to be independent, and would assume it has to do with some family issues (however this would be fairly typical of a boy at his age, so you might want to come up with something tasty for the reader to digest).
Your third sentence could be combined with the second sentence (as it is currently written) using a semicolon; yet I will continue to comment on it as if it were its own sentence. =]
This sentence basically says that the boy doesn't want to force any choice (army-related) on his chimera friend. The boy seems to be dragging the chimera along with him wherever he goes, as of yet the reader doesn't know if the chimera has any choice in anything (being saved or otherwise), so mentioning this would cause the reader to believe that the boy and his chimera do whatever they both agree upon - or that the chimera doesn't have a say, but the boy attempts to do things that would be best suited for the chimera. Slightly confusing there, you might want to edit it or add more information. ^^
Now we have another issue though, because we already determined that the boy is too young to go into the army, but also we don't know what regulations exist for the chimera (or any other mystical beast). So you might want to explain that bit.
Your fourth sentence jumps from all of the previous ideas about the boy being abandoned/rejected by all who knew him, to suddenly having "friends in high places". This also moves a lot of preconceived ideas around...
First off, now the reader has to go back and question the situation where the boy had saved the chimera. If, in fact, the boy is a friend of the Emperor's youngest son, then that would imply that they are relatively close and would likely live in the same city (a rather large city, like the capital city where an Emperor's son would live). This would further imply that a hunter would not be capturing a chimera outside a village somewhere, but instead he's capturing one very close to a very large, densely populated, area that likely has swarms of soldiers guarding the outer walls of the city as well as almost every street within the city. Now we have a problem... how does this boy save a chimera from a hunter? Perhaps the hunter had captured the chimera in a cage and was bringing the chimera to the Imperial Army in order to make it a slave of the army? This would make more sense than previous ideas, though it is unclear as to what happened and how it happened. So you will need to explain this situation to the reader so they aren't completely confused at this point.

Back to the sentence though...
"If it was any helping matter..." definitely needs to be reworded. Try going with something like this: "Fortunately, Tomas had a good relationship with the Emperor's youngest son, who also happened to be the Emperor's favourite son", as it would make more sense.
I like the idea of the eldest son being jealous of the youngest son. Primarily, in a story, you need this type of conflict in order to keep the reader interested in this other character. However, as a reader, I'd like to know how many sons/daughters the Emperor has, and their ages and names (maybe not all at once, but definitely at some point the reader would like to know this information).
And finally... the last sentence of your story (at current, leastwise)... =D
This sentence needs to be reworded, as it is slightly confusing. Perhaps something along the lines of: "The Emperor's eldest son despised Tomas, and any friend of the youngest Emperor's son, was an enemy to the eldest son". (This would help if they had names at this point, lol.) Hopefully you can see what I mean here, though. =]
Overall, I'd say that the story definitely needs more detail and information, but it has a good start and lots of good ideas can come from what you've written thus far. ^^
I look forward to seeing a more completed version, and should most likely not bother you with all of this critique next time.