Ok, let us put evolutionary theory aside for one moment, as there are many who would dismiss it through 'lack of evidence'. and would much rather believe in the 'facts' presented in The Big Book of Fairytales.
However, one thing we can't deny is man's domestication of animals through selective breeding. Hence our insipid pink pigs from wild boar stock; our high yielding milkers -the Holstein-Fresians - from ancient bovines; and our broiler and laying flocks from wild guinea fowl or somesuch.
In the same way that the selectively bred offspring of a wild boar could no longer be called a 'wild boar', but instead a hog or a pig - then the offspring of a descendant of a wild fowl at some point was called a 'chicken'.
Its parent was not a chicken, yet it laid the egg from which the thing we first called a chicken hatched.
Therefore - the egg came first.
It's all about drawing the line between something that is not-quite-a-chicken laying the egg that something that is-called-a-chicken hatched from.
It can also, in evolutionary terms, be applied to the whole taxonomical Class of Aves (Birds).
Taken to its logical conclusion - at some point, something that wasn't quite a bird (as we define it) laid an egg that hatched into something that , although very similar to its parent, was a bird. Therefore, (again), the egg came before the bird.