Since the first chicken probably evolved from an earlier form of similar bird through some sort of mutation, I guess it could be argued that the egg came first.
Genetic mutations can only take place before birth, so technically the egg must have come first.
On the other hand, that first chicken wouldn't have technically been a chicken. It was simply a mutant of the species preceding the chicken.
In order for it to then become a species of its own, it would have needed to develop into a sizeable population.
