I think that the egg came first. The chicken did not exist at the start of time. Thus, the first ever 'chicken' will have hatched from an egg, the mother of the egg not being a chicken, but the animal that the chicken evolved from. So the egg must have come first. I hope that was explained well enough for you to understand.

born or die, which first?

An animal mates with another animal. Their DNA is mutated during replication. An animal is born with these new genes: it is a chicken. Well, evolution and all...but this is simplified.

I prefer the simpler answer. God decided that He'd make a chicken one day. The chicken was a kind of bird, and God had already decided that birds would lay eggs. Why mess with a good plan, right? So God made a chicken, and then it laid an egg. Simple. Why waste time trying to figure out a puzzle that makes no difference anyway? I eat chickens and eggs.

Both male and female chicken first...