The egg, because chickens like all animals (including humans) are constantly evolving so the egg is version 1.4.3.6 instead of chicken before it is 1.4.3.5.
The chicken came first. The modern day chicken came from the egg of an animal slightly different from it. As it has constantly been repeated the modern day chicken egg needs the protein of a modern day chicken. So the most likly answer is that a new generation of chickens were spawned from a few with genetic adaptions to their enviornment. The End.
I say chicken. It's more likely that a something-like-chicken evolved into chicken, than the something-like-chicken had egg, that later became chicken.
Simple, the chilen and all birds ar related to reptiles so when a dinosaur like chicken made an egg, because of evolution, this egg became more bird like until one egg was laid and the chicken is born So egg wins