I’ve always interpreted this as more of a metaphorical question.
However, this general response is where I usually take things if pushed for an answer. Meaning, egg laying species existed for hundreds of millions of years before chickens and chickens evolved from egg laying species, so the egg came first.
A lot of people try to interpret this on the micro scale view: The idea that there was one specific event (place, time, individual) where a non-chicken laid the first egg that hatched out to became the first chicken.
The reality of the situation is counterintuitive, though. Life, nature, and even taxonomy are so much more complex that this situation. It can be hard to conceptualize, but there literally never was a case where a non-chicken laid an egg, and the resulting offspring was the first chicken ever.
The species concept really only applies on a population level (barring exceptions like cases where there’s literally only 1 known living individual remaining of a soon to be extinct species). And furthermore, taxonomy is an artificial, human concept – nature does not abide – and a bit of an art at that. Even if we could somehow scale back in time and view every individual in the chicken lineage as far back as we desire and in much detail as we desired, there would be no consensus on where in that mess chickens emerged from non-chickens.
So, this is one of those cases where I would actually advise – don’t think too hard about it or take it too seriously and accept the question for its metaphorical nature.
Glad to see I’m in good company here with all the Pinky and the Brain references.
When I was growing up, there was one specific commercial – I think it was for Animaniacs – that’s burned into my memory. It was the one where Pinky says something like “Gee Brain, where are we going to find rubber pants our size?”