If refering to the egg in general: the egg! dinosaurs and other primitive organisms laid eggs long before the chicken existed.
If referring to the chicken egg: the egg. The chicken as we know it today (wild chicken, if they still exist) probably descended from a sort of proto-chicken, perhaps with flight, and between the two there's probably a large ambiguous gray area, in which the creatures are neither. The first genetic chicken(s) hatched from one of these gray area-eggs. Thus the egg was first.
(yay logic!)