the egg, of course. lets suppose an ancient "chicken" put an egg, then the "baby" inside the egg, can suffer a DNA mutation that turned it into the modern chicken, but he "ancient" chicken must have been born from an agg to be a "modern" chicken. i know my explanation is messy, but think about it... its really logic!
If we assume that a 'chicken' is a specific animal, recognised by a detailed description of its features, then logically the egg came first. There may have been many chicken-like things, each mutating slightly, but the first thing that was an actual 'chicken' must have been hatched out of a 'chicken egg'. duh.
I wouldn't go with either. It really is my personal opinion that freeflowing genetic material (as well as some protein) came first. it was only after the process of being destroyed over and over again that it developed a solid womb in order to be safe as it matured into a form that it can actually survive which lead to the replication of this through adults of the species so that life will continue into the future. Who really knows, we not even need such a womb to be born, or we may never leave the womb for fear of such danger. evolution can be a scary thought.