Which came first - the chicken or the egg?

The egg.

Obviously the first chicken was hatched from an egg.

The egg wasn't laid by a chicken, but by a lizard ancestor of the chicken. The first chicken was a mutant born of a lizard mother. Same as how the first man was born of an ape mother. Same as the first fish born with lungs was from a mother who did not have them.

Mutation is evolutions way of taking a leap forward.
(Like Picard said in X Men)