Someone told me that the chicken that actually laid the all-important first ever chicken egg had to be a hybrid of some sort due to evolution. Therefore, the first ever chicken as we know it had to come second. Any thoughts?
Evolution does not involve hybrids.
There were many critters laying eggs long before chickens (Jungle Fowl) appeared. Think of the reptiles that gave rise to modern “birds”. Of course man came along and by selective breeding managed to create many types of chickens from the original Jungle Fowl
And reptiles evolved from egg laying ancestors…
The first chicken hatched from an egg laid by a creature that was almost, but not quite, a chicken.
The chicken and the egg are lying in bed. Egg takes a puff of his cigarette, looks over at the chicken and says, “I guess that answered that.”
The Thai alphabet contains 44 consonants with much seeming redundancy: 3 different letters for “Ph”, no less than 5 for “Kh”, etc.; thus identifications like our “A as in Apple” are mandatory.
The very first two letters of the Thai alphabet happen to be “K as in Kai (Chicken), Kh as in Khai (Egg).” Thus the Thais are in doubt about which comes first. 
And hence, the most profound song ever written by man…
(skip to :30 to get to the good part)
Of course, if you’re a strict Creationist, then the chicken came first. You didn’t know it was a religious question, did you?
The rooster.
Egg.
Tris
There’s no real hard dividing line separating chicken from not-chicken, just as there’s no real hard dividing line separating, say, a short walk from a marathon. It’s a soritical situation; it’s a gradient. Every step along the way, the parents are just a little different from the kids, and any iteration you choose to artificially label the breaking point is, well, an artificial choice. There’s no distinguished objective breaking point.
That’s just dealing with “which generation was the first chicken”, but tossing the chicken eggs in as well as alternate links in the chain makes no difference. There’s still no distinguished point of crossover from non-chicken to chicken.
However, the embryo in an egg is genetically identical to the bird it later matures into. So, if you’re going to pick an arbitrary boundary where non-chicken becomes chicken, it must fall on a chicken-to-egg transition and not an egg-to-chicken transition.
The egg came first.
Well, that’s supposing you consider a “chicken egg” to be the egg out of which a chicken hatches. But you could just as well consider a “chicken egg” to be an egg laid by a chicken. I mean, if you’re going to pick arbitrary boundaries, you can do it arbitrarily, right? 
(Which isn’t to say you haven’t made a nice argument, all the same. But the same kind of ordinary language principle that leads us to avoid saying that eggs are chickens, despite genetic identity, could allow us to refrain from saying that eggs which contain embryos which will become chickens are chicken eggs, despite genetic identity)
Why would you define something by its source rather than its properties? If a chicken lays an egg that contains an embryo that isn’t a chicken, then it hasn’t laid a chicken egg, it’s laid something else.
The difference between chicken and not-chicken is genetic. Genetic change only occurs on the chicken-to-egg transition. It’s impossible for a not-chicken egg to hatch into a chicken. But it’s possible for a not-chicken to lay a chicken egg. The egg came first.
Well, its source is one of its properties. But more importantly, even apart form that, one could say a certain genetic makeup, a certain genetic code, codes for chickens which come out of non-chicken eggs. Or even that eggs have important, tangible, genetically-governed properties apart from the genetic makeup of its embryo (I mean, myriad features of the egg structure are governed by the mother’s genetics rather than the child’s, I assume).
But, alright, if you take the position that chicken-ness is a property of genetic makeup in itself (rather than “Codes for chicken eggs” and “Codes for chicken hatchlings”), with chicken-ness of eggs being determined via this from the genetic makeup of the contained embryo alone (and, of course, chicken-ness of hatchlings being determined in the same way from their genetic makeup), then, sure, every chicken hatchling hatched from a chicken egg.
You’d be smug too, if you’d just been laid.
Perhaps his smugness is understandable, but it won’t last for long. He’ll soon discover to his horror that that chick’s his mother!
I think the OP is right (except for the use of the word “hybrid”).
Evolution comes about via mutations. Mutations (even beneficial ones) do not work the way they are depicted in superhero comics. When a mutation occurs, it does not happen all over an organism, it happens in a single cell: it does not change the whole organism (except inasmuch as, in some cases, it will lead to cancer). However, if a mutation happens to occur in a germ cell, an ovum or a sperm (or one of the cells from which these are produced) it may get passed on to offspring, and that offspring will have the mutation in all its cells. Therefore, the parents of the first chicken were almost-chickens of some sort, but one of them had the crucial mutation in the ovum or the sperm cell that lead to first true chicken. A chicken egg was laid, and the first chicken hatched out of it. The egg came first.
It’s relatively simple. Is chickenhood a factor of biology, or are there environmental concerns? If it’s purely a biological matter, then egg, even if we cannot pinpoint the exact egg. If there are environmental factors, then chicken, even if we cannot pinpoint the exact chicken.
Chickens generally not being defined by their high society, it seems pretty fair to go with egg.
Completely agree that it’s an impossible question because of this, but one thing just occurred to me - leaving aside genetics etc for a moment, if we all jumped in a time machine and retraced the ancestry of the chicken in reverse order, I’m pretty sure we would get to a point where I could show you a chicken ancestor and you would say it’s not a chicken, but I could serve you its egg, fried, and you wouldn’t be able to tell.
So in a strictly culinary sense, for time travellers, the egg came first.