But that's irrelevant. The argument isn't about where eggs come from, and simply laying eggs doesn't make something a chicken.
If we define "chicken" as the biological creatures we know today that has a certain genetic makeup, then at some point in their evolutionary history there would be the first such creature that has this makeup being hatched from eggs made by creatures that don't. Just as, at some point in the past, there was the first genetic modern human born from pre-human parents.
Hence, the egg must have come first. This is only an unsolvable problem if you hold that there have always been chickens that never evolved from earlier creatures, i.e. the Creationist model.