So the egg came before the chicken, but the chicken egg came after the chicken. Because the question probably refers to a chicken egg, the answer would be the chicken.
So the only way to solve it is, are we looking for a chicken in any egg, or a chicken in a chicken egg.
I still personally think that the birth of whatever science would class as a chicken, whould happen in the conception and that "chicken" would grow in the egg.
So I would ask again if we care what egg the chicken was in. I reckon its the egg that birthed the chicken who wins. Unless we wanna say the chicken is IN the egg already and so the chicken comes first but thats going too far.