If you buy a pet in China, can you LEGALLY bring it back to the US with you?

Yes you can, but you will have to through the same paperwork as you normally would if you were taking one out of the US. it also depends on the pet, it'll be more difficult to bring some expensive snake then it will to bring back a terrier. However owning the pet might be more diificult in the US as you will have to go through some paperwork there as well. But don't worry you should be able to, for length purposes I won't bother you with the paperwork details but you can easily find such information through your airlines, the US customs, and other organizations that specialize in air travel so most likely you'll be able to.