That’s typically my answer to that question.
I also appreciate the answer that the egg came first because the question doesn’t specify that it’s a chicken egg.
One could argue that the egg predates the chicken by several million years, as the evolutionary development of the egg occurred long before the appearance of the chicken.
Wouldn’t the hen that laid the egg be the one with the genetic mutation or traits that define egg-laying chickens? In this case, the hen would be considered the first egg-laying chicken. Thus, the ability to lay an egg would define a chicken in this scenario, rather than coming from an egg. So, the chicken came first. The chicken that hatched from the egg would be the second egg-laying chicken.
What exactly is a chicken egg? Once you define it, the entire argument falls apart.
Is a chicken egg an egg laid by a chicken? In that case, the chicken has to come first.
Is a chicken egg an egg that contains a chicken? Then the egg has to come first.