I think it might have to do with the 가 at the end of the first word. 가 is a subject marker, meaning that it emphasises the subject (the mouse). Had it been 쥐는, the focus wouldn't have been on the mouse but on the topic/description instead (because 는 is a topic marker). In that case, the sentence would have translated to "there's a mouse under the chair", because the topic (i.e. the question of what's under the chair) would have been what was emphasised.
I'm just learning Korean too, though, so I can't guarantee that this is correct. :)
No, not exactly. If we change the sentence to '쥐는 의자 밑에 있다' then, yes, the focus is more on mouse, but this is probably because the mouse is already the topic of conversation. Like, if you saw the mouse, then lost it and someone screamed:
Where is the mouse?! I don't see it! 쥐 어딘데! 안 보여! It's under the chair! 쥐는 이제 의자 밑이야!
This would make more sense. I actually think the OP's sentence should also be an accepted answer.