Well, a creationist will tell you that God created the egg first and that it hatched and grew up into becoming a chicken.
A big boomer will say that in the cosmic explosion that brought in life to the planet, the most primitive forms of life were the first to appear. Since the egg is more primitive than the chicken, the egg wins again.
If you are more metaphysical than that, still the egg takes the lead because with the egg comes the evolution of the self into a whole being. Hence, the secondary nature of the chicken :)