No doubts

The egg came first. Unless you believe in intelligent design, then some deity poofed the chicken.

Well that’s why it’s a philosophical(?) question. Yes evolution made the chicken, but what would you call what laid that egg if not a chicken first?

If it wasn’t a chicken that laid it, it’s not a chicken egg, so the egg couldn’t come first. What hatched would be a chicken and it would than lay chicken eggs.
- Proto-chicken laid the egg. It was a proto-chicken egg. The creature that came out of it had enough genetic variance to be defined as a full chicken.
  
  Note, the question does not ask "what came first, the chicken or the chicken egg?" It's just "the egg". It doesn't matter what type of egg, as long as a chicken came out of it.
  
  From that perspective, the egg came first.
- What comes between chickens and their non-chicken ancestors? The problem is in our human need to classify everything into different neat boxes, when it's an actual long and continuous process. In short, the "dilemma" created is more of an argument about what separates species, and that's a hell of a rabbit hole with no single answer.
  
  But the answer is the egg, since a chicken born from that egg is different than its parents.

Two answer.

"Chicken" comes before "or the egg."

Or

Whatever layed the first chicken egg was not itself a chicken, but a few tweaks of the genome away. I this regard, the real answer is "The egg."

The egg since eggs existed long before the first chicken. Since the question does not specify it HAS to be a "chicken egg" just egg
Definitely the correct answer.

Unless scientists decide chickens are still the same species as their wild counterpart (the red junglefowl), like with dogs and arguably pigs.

Probably won't bother, honestly.

The problem with this question is that its assumption is so wrong that it is rebdered meaningless. Chomsky once wrote the sentence “Colorless greed ideas sleep furiously” as an example of a sentence that has syntactic correctness but no semantic meaning. Also, why a chicken, in particular? Why this animal who has been so successfully domesticated and differentially bred over centuries that calling it out is like Roy Confort calling out the similarly domesticated banana as evidence of god and creation?

In any case, eggs came first. The egg, if you will, is basically a big cell. It has a lot going on, but it got figured out long before modern birds, much less the domesticated chicken.

But of course, that’s not what they really mean. What they really mean is - how do you get from not-chicken to chicken without the biological equivalent of a big bang (and I’m not even touching on how cosmogenesis gets misunderstood)?

And the real answer is that, whether we’re talking about natural or human driven evolution, there’s no line between chicken and not-chicken. Its fairly easy for us to say that a cat is not a chicken and that a jellyfish is not a chicken, but as you get into the later dinosaurs and early birds, you start to move into grey areas.

Which brings us back around to semantics. As humans, for some reason, we like hard categories around things. That’s often not how the real world works. There’s really a lot of just continuous blessings, and ideas like species are a convenient label for us to understand gross differences but whose utility starts to fall apart once too closely examined. The definitions written in textbooks for high school students are unhelpful, as they represent the ideas as if they were handed down from on high, rather than “this is a convenient way of organizing things for some of our purposes.”