I think, that the chicken came earlier than the egg, because chicken is something that was evolved. It happened slowly, not instantly. When the chicken was evolved like it is now, it started laying eggs probbably.
Meh idk really.
The answer on this is very simple, if you know how evolution works. The egg came first. The bird that laid the egg wasnt a chicken but a close ancestor of the chicken, because of natural genetic mutation the DNA of the egg it laid was different of the bird that laid it. The egg hatched and there was the first chicken, who came out of the first egg.