Is cosmetic surgery on your chest possible?

Yes: Depending on what the nature of the problem is. Please consult with a plastic surgeon.

Yes, but : Yes, but not advisable.

Depends: Depends on what you want to change. The question is far too vague for any other answer.

Chest : That is very nonspecific question. There are many procedures that are performed on the chest. Some are cosmetic while others reconstructive. You should see a board certified plastic surgeon.