The chicken. No wait, the egg. Hang on a sec. Is this a trick question…?
Actually I like the line by Peter Medawar (a fairly famous scientist who worked on the immune system and wrote some great popular science books): “A chicken is an egg’s way of making another egg”.
More seriously it’s a hard question to answer because it asks us to look up a moment (or more likely an era) in evolution that we can no longer access. Birds are related to dinosaurs which also reproduced by laying eggs. So what came before them? I don’t know enough about evolution (and earlier species) to be able to help you much.
The egg. Dinosaurs (and other reptiles) had eggs with shells long before birds evolved.
Which came first the chicken or the chicken’s egg. Evolution would suggest that the chicken gradually evolved from a very chicken like ancestor, so I think it would be impossible to say exactly when either chicken or chicken’s egg evolved.
Sometimes we humans get hung up on the idea of drawing boundaries between different categories when in nature there is in fact a smooth continuum with no dividing line. I think this is because we like to speak write and think in words (which, if they mean anything seem to require clear edges – this is a chicken, this is not a chicken). I think this leads to a lot of reasoning errors.