For arguments sake, if the emergence of a species can be given a definitive point in the evolutionary line as a final set of mutations particular to one generation which is absent in the previous, then the important factor is the DNA itself. The DNA of the parent is "not-chicken" whereas the DNA of the offspring is "chicken." Under this interpretation the "chicken" DNA is present first within the embryo contained within the egg. (While this embryo is technically a chicken, the "chicken or the egg" question is specifically referring to an egg and an adult chicken.) Presumably there has not been enough genetic mutation since this point to warrant the emergence of a new species by the guidelines laid out above, as such this egg is identical to those laid by the chicken that hatched from it and so on. Therefore, while it was an egg laid by a "proto-chicken" it was in fact a chicken egg.
The egg came first.