The chicken or the egg was an example of temporal paradox, more specifically an examination of causality, and also became an expression used in discussing the nature of time.
The question, "What came first, the chicken or the egg?", was a paradox, as chickens were hatched from eggs, which were laid by chickens. So the existence of one ensured the existence of the other, but which started the process was a mystery.
The Free Lunch theory answered this problem by suggesting that both the chicken and the egg came into being at the same time. (PROSE: Falls the Shadow)
When Fyodor Nikolai Kerensky managed to hatch an egg and get the baby chick to grow fully in seconds, the Fourth Doctor asked this question. (TV: City of Death)
The Seventh Doctor entertained the Gods of Ragnarok with a magic trick where he drew eggs from his mouth, after first asking, "How did life begin? Was it with the chicken, or..." The Gods seemed unfamiliar with this concept. (TV: The Greatest Show in the Galaxy)