Nimble (Ex): The master chymist’s lithe physical frame gives her an alchemical bonus on all Dexterity checks, Dexterity skill checks, and CMD, and a natural armor bonus to her Armor Class. The bonus is equal to half the master chymist’s class level.
|MrCharisma|It would be an Alchemical Bonus, which is the same bonus that you get from Mutagens.
They give their bonuses to different things.
Mutagen gives an Alchemical bonus to your Dexterity score. This bonus translates to a bonus to your ability modifier. You apply your ability modifier to a Dexterity check.
Nimble doesn't affect your ability score at all, so it stacks just fine with Mutagens etc.
EDIT: I just re-read your question, ignore the above.
It's an untyped bonus, so they should stack. They seem to have very specifically written it so that it will stack.
SECOND EDIT: Now I'm not sure. Let's see what someone else comes up with =P