Here's a new wrinkle in the debate.
Egg first:
God created birds, man then did the selective breeding thing, the right cross produced an egg, and out popped a chicken.
Life crawled out of water, went back into water, figured out that an egg was a way better process than finding water again.
Chicken first:
God created birds, man did the selective breeding thing, the right cross produced an egg, out popped a chicken, and it laid the egg that produced more chickens.
Life crawled out of water, went back into water, figured out that an egg was a better process than finding water again, evolution did its magic, and out popped a chicken.
New wrinkle
The egg and chicken as we now know it both arrived at the same time. The jungle fowl were selectively bred. Due to this selective breeding process and genetic mutation/manipulation, an embryo complete with surrounding egg material formed in a jungle fowl hen. She did her version of a chicken egg song, looked in the nest and thought what a funny looking big brown egg. 21 days later this instantaneous development of chicken egg and chicken hatched out and chicken math was created.