Biblically, the chicken must have come first. I can't imagine God making an egg and dropping it somewhere in the garden of Eden to fend for itself. The logical thing would be to make a fully grown chicken the same way he made a fully grown man. But that's the biblical point of view.

In terms of evolution, the egg would have come first. Modern day birds evolved from reptiles. Studies show that modern day birds evolved from a prehistoric species called theropods. Through generations of theropods laying eggs and each generation slowly resembling birds more and their parents less, the Archaeopteryx was born. It was the first animal to be considered a chicken, even though it had reptilian features such as teeth and claws. It resembles the modern day chicken more than it resembles reptiles. So from evolutions point of view, the egg came first