Time for some fun here
So is it any egg or specifically a chicken egg? If it is any egg then the egg came first because there are fossil records from the period before chickens existed. However if it is a chicken egg then we have to define chicken egg. If you define chicken egg as an egg laid by a chicken the chicken came first, but if you define a chicken egg as an egg from which a chicken emerged then the egg came first.
Question answered, now time for pictures