Eventually, this goes to creo vs evo (like most debates concerning living things usually do).
If you're a creationist, chicken was first because they were created. That's quite obvious because even God (despite His obvious lack of common sense in some cases) couldn't be so stupid as to waste his holy infinite energy to first make an egg, keep it warm until it hatched and then take care of it until it got big enough to feed itself, no sir, He would have made the chicken ready once and for all IMO (should there have been a creation...)
If you're an evolutionist like I am, the egg was logically first, because the first bird that could be qualified as a chicken was logically borne as an egg laid by a "pre-chicken" bird, a bird that couldn't yet be qualified as a chicken.
More specifically, the first chicken was the bird that lacked the ability to reproduce with the species from which the chicken originally derived from via specifiation.
So, first there was a pre-chicken population of birds. Then one part of that population was separated from the other part of population, and started to evolve onto chicken-ish direction. When the first member of this separate population differed enough from the original population (ie. couldn't reproduce with the original population but only with its own part of population), it was the first chicken and it was the same chicken inside the egg, thus the egg was first. The bird that laid the first egg was not yet a chicken, but its ancestors were (and are) chickens.
In short, a non-chicken laid an egg that contained a chicken that had evolved from the non-chicken via mutations.
Not that it matters any bit, but the problem was actually solved many many years ago.
