The earliest lifeforms to lay eggs appeared between the Cambrian and Ordivician Periods of the Paleozoic Era - around 500 million years ago. Birds did not evolve until the middle Jurassic Period of the Mesozoic Era, some 300 million years later, and I somehow doubt that these proto-avians were anything like the modern day chicken.
The egg came first - stop wasting your time and move on to the next question.
