Yes, it's easy to imagine that chickens have idealistic lives on farms. We know that in reality they get cramped into tiny spaces in which they can barely move their wings, while they get pumped full of hormones to make their breasts giant. "The Chicken of Tomorrow" looks ridiculous now that we know all this. So it makes perfect sense that "Mystery Science Theater 3000" tore the movie to shreds. The Satellite of Love crew has a lot of fun with the short.
Oh, and what I mean by my title is that the answer to that age-old question is a simple matter of understanding evolution. Birds evolved from dinosaurs. Therefore, the a dinosaur had to lay an egg one day, and out hatched a avian. It's really easy when you think about it.