Neither came first. One day, long ago, a little adult dinosaur poked his head out of his hole and said to himself, "Well, I think I'll evolve into a chicken today." This was a noble and worthy goal, so he climbed out of his hole, closed his eyes, and concentrated very, very hard on becoming a chicken.
Suddenly, his scales enlongated and POOF! suddenly they were feathers! His nasty little teeth and lips became pointed and hard and became a beak. He knew he was halfway to becoming the Pride of KFC!
However, muttering to himself like he'd been doing had attracted the attention of a prowling Allosaurus, which ate him as a snack on her way to the rotting carcass of an Apatosaurus.
What we call "chickens" are actually miniature polled elk. What we call "eggs" are actually seperate creatures which appear spontaneously under miniature polled elk.