Everytime this conversation is had I come in with the "but actually, evolutiuon explains this" argument so I'm both surprised and happy to see others make that too. Like you said, the egg isnt just going to come into existence all on it's own. Since it's a cyclic process of minor changes over generations, it's not a clear cut answer because modern day chickens didnt just show up one day, they likely evloved form some premitive animal and they will continue to evolve so maybe like a millennia in the future you can have an argument about "what came first the (insert animal that evolved form chickens) or the egg"