Which came first? The chicken or the egg?

The egg.

The humble chicken (aka Gallus gallus domesticus) is descended from the Red Junglefowl (Gallus gallus, for those playing at home).

The event that led to the separate chicken species, was the domestication of the Red Junglefowl, 5000 years ago in India. I'm not exactly sure how you go about domesticating wild birds, but lets assume you take an egg from a Red Junglefowl and then let it grow up in captivity. In that case, the first chicken egg was laid by a Red Junglefowl. So the egg came first.

Unfortunately, there is no clear definition of what constitutes a separate species. The first chicken probably looked identical to a Red Junglefowl. The line between species is arbitrary.

The point is, the chicken and egg problem is all thanks to some guy in India who couldn't keep his hands off the wildlife.