Ok, so.. For a long time, I've claimed that obviously the egg came before the chicken, as the first chicken had to be hatched from something.
We had a discussion about it today at work, and Jens contested that claim. So now I've revised my position.
Chicken can lay eggs without them being fertilized. This means the eggs are made up of non-genetically-mixed material, and that the fertilization alters the contents of the eggs (the thing that gets hatched).
This means that some kind of proto-chicken got fertilized, laid a proto-chicken egg that contained a mutated offspring that we would today call a chicken.
So obviously, the chicken came first. QEFD.