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.”