I don't see it like that exactly. Theoretically speaking you could decide the exact criteria for what sort of bird qualifies as a chicken and then go back in time to find the earliest individual that meet all the criteria. The mother of that chicken would then not be a chicken but some other more primitive species of bird.
This is how it most likely happened. At least it follows the evolution logic. The exact point of when we stop caling it a thingamajig and start calling it a chicken is the key, but it still means that the chicken was first and then the chicken created the egg.