This is a good question, and one that has plagued mankind for centuries. Indeed, which did come first? On one side, you have the egg advocates, who say that you cannot have a chicken unless it hatched from an egg. On the other side of the debate are the “right-wing” chicken experts, who say that you cannot have an egg unless a chicken lays it.
I can answer this question very simply–no other animal described in the creation account in Genesis began in the embryonic stage. It is safe to assume that God created the chicken first and then the eggs were sure to come. Just remember: don’t count your chickens before they’re hatched.