Graham is correct, well played.
Short answer: the chicken had to come out of an egg, but that egg didn't come out of a chicken.
Unnecessarily long answer:
1. Assuming (for one brief, glorious moment) that we agree on evolution, we accept that that all living things evolve through changes in their DNA.
2. So one day a male not-a-chicken meets a female not-a-chicken; they chat (not online, amazingly!), dance, fall in love, hit a rough patch while they rile each other about how crap the other one's native land is, and then just say to hell with it and toss a coin to decide where they're going to live, go through an expensive and tedious visa application process. And then the sweet love-making begins.
3. So DNA (cue Jurassic Park segment) from the male not-a-chicken and the female not-a-chicken combine and form the first chicken zygote. That one zygote divided to produce the first true chicken.
4. And it was finger-lickin' good.