It's not interesting even when you don't intentionally misinterpret it. If a chicken egg is an egg from which a chicken will hatch, then the egg came first by definition. If a chicken egg is an egg laid by a chicken, then the chicken came first by definition.
The very nature of evolution on macro organisms is very gradual changes.
Reminds me of the futurama joke around the "missing link"[1].
But that has no effect on the answer to the question. Given the definition, it is not necessary to identify the first chicken in order to know whether that first chicken hatched from the first chicken egg (definition 1) or laid it (definition 2).
If God put chickens on the Earth then they came first obviously.
If chickens evolved from some close but not quite chicken ancestor then the first chicken hatched from an egg with a beneficial genetic mutation.