Your conclusion makes it sound like God and science are contradictory, but that's not necessarily true.
I have discussed this with many people before, and this is the all around conclusion!
Religious beliefs say that the chicken came before the egg because god made him.
Evolution says that the egg was mutated and formed a new breed.( Such as with humans and apes - minus the egg.)
This means that if you decide to take a step toward God with your decision you will conclude that the chicken came first.
If you take a step toward science in your decision, you are taking the evolutionary path, and therefore the egg came first.