I’m going to try to give you an actual answer to your question as I believe you intend it …
First: Let’s agree that the question being asked is NOT “did chickens or eggs exist first?” but rather “If chickens lay chicken eggs, and chickens are born from chicken eggs, and any egg not in this category is not a chicken egg, then is this not a paradox? If there was no chicken, how could a chicken egg be laid? And if there was no chicken egg, how could a chicken be born?”
The “real” answer: What this question actually demonstrates is a weakness in language. It is an ambiguity in the term “chicken egg”. It leaves open for interpretation by the listener what a “chicken egg” actually is, what makes it a “chicken egg”. On the one hand it could be “eggs produced by chickens”. It could be “eggs from which chickens hatch”. It cannot actually be both; they are different, though in practice only slightly. So the answer changes based on how you define “chicken egg”.
My “best effort” answer: If I want to try to answer the question literally, I define “chicken egg” as “An egg which, if allowed to hatch, reach maturity, and breed, will likely produce another of itself (i.e. another chicken egg).” In which case the answer is clear: the chicken egg came first. There was a proto-chicken, something very much like a chicken but not quite a chicken. It laid an egg with the genetic mutation that made it a “chicken egg” instead of a “proto-chicken egg”. And thus began chickens.
I’m going to try to give you an actual answer to your question as I believe you intend it …
First: Let’s agree that the question being asked is NOT “did chickens or eggs exist first?” but rather “If chickens lay chicken eggs, and chickens are born from chicken eggs, and any egg not in this category is not a chicken egg, then is this not a paradox? If there was no chicken, how could a chicken egg be laid? And if there was no chicken egg, how could a chicken be born?”
The “real” answer: What this question actually demonstrates is a weakness in language. It is an ambiguity in the term “chicken egg”. It leaves open for interpretation by the listener what a “chicken egg” actually is, what makes it a “chicken egg”. On the one hand it could be “eggs produced by chickens”. It could be “eggs from which chickens hatch”. It cannot actually be both; they are different, though in practice only slightly. So the answer changes based on how you define “chicken egg”.
My “best effort” answer: If I want to try to answer the question literally, I define “chicken egg” as “An egg which, if allowed to hatch, reach maturity, and breed, will likely produce another of itself (i.e. another chicken egg).” In which case the answer is clear: the chicken egg came first. There was a proto-chicken, something very much like a chicken but not quite a chicken. It laid an egg with the genetic mutation that made it a “chicken egg” instead of a “proto-chicken egg”. And thus began chickens.