Science:
The "hen" came first. However the hen did hatch from an egg. The reason that the hen technically came before the egg is that the hen did not hatch from a "hen" or "chicken" egg. The first hen would have been a slight variation of a parent species and would have been the first to share adaptations (Which at the time would be considered mutations) that are developed enough to constitute a new species. So via speciation the hen would have emerged from a non "hen" egg. Later then, that hen would hatch an egg, or move onto the process of hatching the first true "hen" egg.
Popular Religious/cultural implications: The "hen" appeared before the "egg" as it was created in entirety by a deity or supernatural force.
Unpopular Religious/cultural implications: In some cultural and belief systems the egg was created that later hatched the chicken, and in some cases many other species.