If you didn't have a chicken or something like a chicken first.... How did u get the egg? 
You had something like a chicken, (theropod dinosaurs), that laid eggs in a radioactive environment which caused mutations.  Of course, this begs the next question of which came first - the dino or the dino egg?  And that takes us back to primodial slime, (biological 'soup').  Where'd the soup come from, you may wonder?  Odds are it wasn't from a deital 'grandma' but, from meteoric impacts which carried the dormant cellular components.  Now, as for where these dormant cellular components came from ...