An individual animal does not evolve into a new species during its life. Evolution works through variation in offspring. So the first bird that we would call a modern chicken must have been born a chicken and came from a chicken egg that was laid by the last in a line of animals that were the evolutionary predecessor to the modern chicken. So in that sense, the egg came first.

But evolution is a slow and gradual process. The evolution of chickens took place over millions of generations, so we can’t pinpoint a single moment when the first modern chicken was born. To confuse the issue further, there are actually great genetic variations in every generation of chicken, sometimes to the extent that we classify animals into subspecies. And what we classify as a “chicken” today is different than what we would have called a “chicken” just 2000 years ago. So it becomes impossible to suggest that an actual specific non-chicken laid the very first chicken egg. But no matter the definition of the first “chicken” it most surely came from a “chicken egg.”

That’s what you were asking, right?