My stance is that creatures were laying eggs millions of years before the first chicken was born.

That was never a "serious" question in that sense. It's just a philosophical paradox.

The real answer is that you need to look at the ancestry tree. There wasn't a moment that a chicken popped up, it was a gradual evolution between an ancestor and until a point that we decided "yup, that's a chicken".

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.

People are confidently saying that the egg came first. But the answer really depends on the askers definition of what a "chicken egg" is. Is it an egg that a chicken hatches out of? Or is it an egg, laid by a chicken? If it's the former, then yes the egg came first. If it's the later, then the chicken came first.

something that was not a chicken made a chicken egg

Eggs were around long before chickens. A chicken can't exist without an egg, an egg can exist without a chicken.

i always assumed this was a rhetorical philosophical question, not any actual line of "scientific" enquiry.

The rooster came first, of course

The answer is pretty obvious if you know and understand evolution. Something that wasn't quite a chicken laid a chicken egg and hatched the first chicken.

If you're talking about the chicken and egg problem in the abstract, i.e. how do you determine "what caused what" in a system that feeds back into itself... the answer is that in feedback systems, determining blame or ascribing one or the other as the cause is simply meaningless, and you need to examine how the system behaves as a whole, and how the different parts contribute to the output of the system in various configurations.

Yes, it's the egg. Eggs existed long before anything resembling a chicken existed.

The super-dimensional beings that wrote the chicken script came first.