This is a question that is probably as old as chickens, and it has been puzzling philosophers and schoolchildren for ages. Both Socrates and Confusious have asked which one came first (Source: I made it up). But I'm here to settle it once and for all!
The Egg
The egg came first. Eggs evolved around 325 million years ago, while chickens date back around 4-10 thousand years. These numbers might not be exact, but it's clear that one came a lot before the other. So that's it! Although this is hardly the question that is actually being asked (or at least meant to be asked).
Which Came First, the Chicken, or the Chicken Egg?
This question seems a bit harder at first glance, since it's the question that people actually mean to ask: If the chicken egg came first, then who laid the egg? Well, a chicken. But where did that come from? Well, a chicken egg. And so on ad infinitum.
It is, however, upon a moments reflection clear where the problem lies. The word 'chicken egg' is here being defined in two ways, as 'an egg laid by a chicken', and 'an egg containing a chicken'. This confusion is understandable, since these two rarely come apart in our everyday experience (eggs laid by chickens usually contain chickens, and vice versa). How you define 'chicken egg' is, however, crucially important to how you answer the question at hand (of course, how you define the terms in a question is always gonna be crucial to how you answer it, however, 'chicken egg' is the only really problematic term here).
Choosing a definition of 'chicken egg' is quickly gonna resolve the question. If you define it as 'an egg laid by a chicken', then it is clearly the chicken that came first, since there had to be a chicken to lay the first chicken egg. If, on the other hand, you define it as 'an egg containing a chicken', then the egg clearly came first, since there didn't have to be a first chicken to lay the egg, and the first chicken was thus contained in the first chicken egg (you could also say since the egg is defined in terms of containing a chicken, and since the first chicken (probably) came from some egg, then the first chicken by definition came from the first chicken egg, and since the egg was there before hatching, the egg came first). So there you have it. This age old question is resolved. Unless...
Do Chickens and Eggs Exist?
Remember when I said, that 'chicken egg' was the only really problematic term here, just before? "'chicken egg' is the only really problematic term here". Well, I was LYING. Both ‘chicken egg’ AND ‘chicken’ are problematic. Why? I think, to see this, it helps to ask another question: When was the fist chicken? It quickly becomes quite clear, that this is a very difficult question to answer. Not just because we can't go back in time and look, but also because it's not clear what to look for. If we find a candidate for the first chicken, then why not one of its parents? What difference is there between this one, and its parents, that qualifies it as a chicken, and the others not? It's gonna be very hard to point to a clear difference. This, it seems, is gonna be the case for any chicken we pick as the first. The keen reader will notice that what I'm getting at is a sorites paradox.
We will set up an argument as follows:
Creature X is not a chicken
If Creature X is not a chicken, then Creature X+1 is not.
If Creature X+1 is not a chicken, then Creature X+2 is not.
…
If Creature X+n0 is not a chicken, then Creature X+n1 is not
Here Creature X is just gonna be some creature, that we can all agree is not a chicken, and thus premiss 1 is true by definition (in a dialectically relevant sense, since it is agreed upon). X+1 just signifies that we have moved one step down the family tree (such that Creature X+1 is an arbitrary child of Creature X), and this of course carries on to X+n. Premiss 2 seems plausible, since you are not gonna be able to point to any relevant difference between the two. But this leads us down a slippery slope, where you are not gonna be able to say that any creature is a chicken (assuming we picked a Creature X, which is an ancestor of what most people would call chickens today).This argument could of course be run in reverse too, leading to the conclusion that all ancestors of chickens are chickens.
How does one get out of this sticky situation? There are a few possible responses, although I will mostly highlight my preferred response. One possible response is the obvious one of just choosing a stopping point, for an example: The first chicken is Creature X+5313. This is of course very implausible. Why this number and not any other? Another way is to say, that some things are definitely not chickens, like Creature X, while some things are definitely chickens, say Creature X+6092, while the ones in between are neither chickens nor not chickens. This, however, just kicks the can down the road: How do you choose the boundaries for when it becomes indeterminate whether a given creature is a chicken? Now you have just added extra unnecessary vagueness. These responses, and more, could all be fleshed out and discussed a lot more, but I will now present the response I find most plausible.
I largely follow Michael Huemer in his semantic nihilism. Basically, I take it, that vague terms, like chicken, do not have truth value, in other words: They cannot pick out something in the world, and thus cannot constitute propositions. So when I say “the chicken came first”, I am actually not expressing a proposition. This view is virtuous in several ways: It of course explains what is wrong with the sorites argument (it is not sound, since the vague sentences fail to express true propositions). It also preserves classical logic, since you do no need to introduce glutty propositions, rather you just say that the sentences that include vague terms do not express propositions, thus preserving the law of excluded middle. It is also a very simple solution, in that it is not arbitrary; all vague sentences fail to express propositions. This of course means that the vast majority of sentences in natural language fail to express propositions, since the terms used are vague. This might be seen as a problem, but I think it is really not much of one. Sentences can still have meanings, in the sense that they express intentional attitudes of the one who utters them. When I say “that is a chicken” about an object I see, the sentence still has meaning in the sense, that it is about the chicken-shaped object of my perception. This can be true, while still maintaining that the sentence could not be used in a sound syllogism. It also makes sense that natural language would not be made to pick out propositions. Natural language is presumably developed to be useful, and not truthful, and it would thus make sense that the categories in natural language would be useful, but not necessarily truth tracking. Other examples of this could also be cited, like metaphors, hyperbole and so on.
The Answer
So my answer to the question “Which Came First, the Chicken, or the Chicken Egg?” is: There is no answer, since both ‘chicken’ and ‘chicken egg’ are vague terms, and thus an answer containing these terms could not express a proposition, and thus not be true or false.