The bacteria :) Okay, so it wasn't really a bacterium, but "the primitive cells that modern-day organisms evolved from" doesn't have quite the same effect.

I wouldn't say that there was ever a "first chicken", as evolution is a gradual process, and there's really no clear line when one species becomes a different species. So I really don't think there was ever a time when an organism that was not a chicken laid a chicken egg. The concept of a species is relevant in considering evolutionary linage if you're looking at discrete time points that are reasonably far apart on an evolutionary time scale, but not really for looking at consecutive generations. If there were a "first chicken," then that chicken would have to mate with a pre-chicken, so their offspring would be a mix of chicken and pre-chicken, which if those are two different species would have to be yet another species, and therefore not a chicken, so the next generation wouldn't have any chickens at all, and any future chickens would have to be the offspring of pre-chickens. Since chickens and pre-chickens would at that point comprise a single population of interbreeding organisms, calling them separate species wouldn't be appropriate. It's like saying black house-cats and orange house-cats are two different species, or that people with different blood types are different species. When two populations of similar organisms become separated, each gradually accumulate traits that are different from the other population, and eventually they might be different enough that there's no doubt they're separate species, but if they're in similar environments, it hasn't been that long, or there's some migration between the two populations, it's not always clear whether they should be considered separate species or not.

Although, an egg is just a female gamete, it doesn't have to be from a chicken, so wherever chickens started to be chickens, eggs definitely predate that by a lot.