Actually 'me' this dos not necessarily work. Technically this question has several variable factors but the most important one is when do we define a chicken becoming a chicken? Because of Darwin's theory of evolution all animals have evolved over many millenia to what we see today. Some people in the comments section use this incorrectly to explain their point. Chickens evolved from dinosaurs and Dinosaurs laid eggs so the egg came first, wrong because a dinosaur would not simply lay a chicken as we see it today as that would take many millions of years not one generational lifespan. Additionally if we count dinosaurs as being the chickens predecessor then what came first- the dinosaur or the egg? All animals came from single celled ameobas at what is affectionately called the primordial soup. Therefore if we look at it logically the chicken, or rather the original chicken came first way before the egg which would have been developed later to protect offsping form the evolving predator.

If you would like to look a this through a simple perspective simply ask yourself where the egg came from. The egg is simply a transitional phase from conception through to growth outside of its mother. A chicken would be much more likely to survive on its own from predators with the benefits of sight and motion rather than being stationary and unaare of its surroundings. The species if it wanted to survive would have to had risen from a defendable creature rather than an undefended (from larger stronger predators) external womb. (the earlier a creature can 'fight of flight' the better, the longer it stays undefendable the more likely it is to be eaten).