I would say:
The chicken is the last in a very ancient history of creatures who were successful random mutations of earlier species. The first chicken came from a mutated egg of something not quite as chickeny, and so on, until the least-chickeny semi-chicken… since the mutation in question happens in the egg, the first chickeny-anything was an egg, and the first fully-chicken was an egg.
But if you mean “the egg” rather than just “the chicken egg”, then clearly the egg is massively older than the chicken, because all sorts of creatures have eggs: other birds, reptiles, fish, insects, spiders… etc.
(p.s. I didn’t notice @SavoirFaire‘s more scientifically-worded answer already above.)