The two that birthed the egg that would grow into the first chicken were not chickens, but some previous form of chicken relative that may or may not still exist today. All we know about them is that they were not chicken-like enough to be considered "chickens" by modern standards. However, genetics made it so that that egg could be considered a "chicken" by the same standards. Therefore, assuming from the nature of the question at hand that a chicken still in the egg is not considered a chicken, the egg came before the chicken.
Of course, this all assumes that our definition of an "egg" does not include eggs of other species, as well, or else this question would be obvious.
I never really bothered with people much. Maybe I can learn.