Wouldn't it just be a reptile then? If two different species mated together to create offspring then they would have created a new species. The offspring had to be born first and had to be significantly different from both species to be considered a new species of it's own. Then THAT generation would lay the first eggs.

(Unless we go the religious route and say that god created all living animals blah blah [this explination doesn't count])

Personally, I think that Chickens are just evolved dodo birds.