Egg. It's basic genetics.
The theory of evolution suggests a slow mutation leading from a specie to an other. (I say "suggests" to be rigorous, Science never proves, it suggests things and those theories stay plausible until proven wrong. But Evolution is my strongest belief, if you are a creationist, you will disagree with me)
We know dinosaurs laid eggs, some of them were able to fly, and birds species come from them.
With this slow evolution, the first chicken (as we know it) came from an egg laid by a specie close to the chicken we know.
There is no genetic change possible between the moment the egg was laid and the moment it becomes a chicken. So, the egg was first.
I hope I explained it clearly enough, it's hard to do it in English for me!