This is a false dichotomy; there was no "first" chicken or egg
Eggs, as we know it today, did not simply come into existence overnight, and neither did the modern chicken. Both of them were the result of centuries of evolution.
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There is no hard definition of what is a chicken and what is an egg. Like every other living organism, chickens and eggs have evolved over time, and each stage of this evolution could be called a chicken, and each stage of this evolution can also be called something else. Millions of years ago, chickens evolved from a group of dinosaurs called the theropods. The original species of “chicken” started with claws and teeth on their wings and evolved to the modern “chicken” that we see today. However, between the theropod and the modern chicken, no turning point made the chicken “the chicken” and made the egg it lay “the egg”. Chicken and egg are constantly evolving terms, and unless one can draw an arbitrary line on where exactly this modern species began, there would be no way of telling whether the egg or the chicken was the first one created after that line was passed. Even today, chickens and eggs are different from each other. One chicken is not more of a chicken than another, and one egg is not more of an egg than another. The chicken never came before the egg, and the egg never came before the chicken, because neither the egg nor the chicken actually exists as a term. Yes, the theropod chicken would have come before the gallus domesticus egg, but the theropod egg also would have come millions of years before the gallus domesticus chicken. And even if one were to just measure from the beginning of gallus domesticus chickens and eggs, there still isn’t a first chicken or first egg that was pointed towards and classified as gallus domesticus.
The term chicken and egg is not absolute because every term that exists will mean something slightly different to different people. However, simply because a term isn’t 100% agreed upon doesn’t render that term unmeaningful and false. There is no exact definition of what jeans are, for example, and what qualifies as jeans, but most people can still agree that jeans were invented by Jacob Davis and Levi Strauss in 1873. Furthermore, even if there have been many types of chicken-like creatures, that doesn’t mean that the origins of the modern chicken, or the gallus domesticus, is completely unmeasurable. We have modern samples of their eggs, their genetic traits, reproduction cycles, and all other information needed to investigate their origin. Most origin tests on this issue have also been done on the gallus domesticus. Maybe there comes a point where we trace chickens so far back that we simply conflate them with dinosaurs that have developed tiny wings, but that doesn’t mean that this question is an absolute false dichotomy and can’t even be answered for the most basic farmhouse chicken.
[P1] "Chicken" and "egg" are permanently evolving living things that have no static definitions. [P2] It is impossible to compare two undefinable terms; therefore, this question has presented a false dichotomy.
Rejecting the premises
[P1] Even if many types of animals have been predecessors to chickens, the modern farm chicken can still be investigated. [P2] Most terms' exact definitions are up for debate, that doesn't mean we cannot discover their origin or trace their history.
- https://www.levistrauss.com/2019/07/04/the-history-of-denim/<ref name=jeans>https://www.levistrauss.com/2019/07/04/the-history-of-denim/