I don't think the question is whether any egg came before any chicken. That's obviously an egg, as you are implying. But the question is really, I think, what makes an egg a chicken egg? Is it an egg that is laid by a chicken or is it an egg from which a chicken hatches?
An egg laid by a chicken is also an egg from which a chicken hatches, unless significant mutation. An egg from which a chicken hatches could be a mutant laid by a non-chicken. But it's a bit sorites heap trying to decide which mutation makes the non-chicken a chicken.