Is it an egg that came out of a chicken or an egg that has a chicken in it? You've defined the chicken egg as an egg with a chicken in it, so I'll agree that the egg came first. But that egg was laid by the something else that was its immediate predecessor, so it could be considered to not be a chicken egg, which could be used to say the chicken came first, but whatever.
randman has demanded ad nauseam the "transitional" species, essentially wanting evidence of one species giving birth to another. If the first chicken in an egg was not an egg from a chicken...voila!