This question will actually tell you about the philosophies of the responder. If they follow a creationist line of thought, they'll reply chicken, and quote the bible. If they follow an evoloutionist line of thought, they'll say that eggs were in the fossil record long before chickens.
I say eggs, because breakfast comes before dinner.
If the egg came first you would need a hen to lay and hatch the egg. If the chicken came first, well it depends. Was the chicken a Hen or Rooster? If it was a rooster there would never be an egg. If it was a hen her eggs wouldn't be able to hatch. Honestly neither
Yeah like someone said, it depends on what your beliefs are, do you believe in evolution, or do you believe God put these animals here for us. If you believe that God is the reason, than Wouldn't it be a little strange for a lot of eggs to be left here. Rather than birds. The earth would get pretty stinky with ALL those rotten eggs.