Before there were any chickens, there were, going backward in time, reptiles, amphibians and fish, all laying eggs. Probably there were other bird eggs too, before there were chickens, as the chicken was probably not the first bird to evolve--more like an archaeopteryx.

If it's specifically meant a chicken egg, rather than just any old egg, then one has to make a fine distinction as to what is a chicken.  If one makes the distinction very, very fine, then the last mutation that gave rise to chickenhood, would have been in the reproductive cells of a non-chicken, which then laid the first chicken egg, which then grew up to be the first chicken.