A female ${animal that came before a chicken} produces a mutant egg which can be said to be a half-chicken. Did that egg count as a chicken egg?

This is a fairly interesting question by itself, but I would offer two objections with regard to the original question:

1. Any egg that would produce something that would be considered a chicken is still an egg.

2. The OP doesn't stipulate any kind of egg, and we can probably safely assume that any direct ancestor(s) to a chicken also reproduced by laying eggs.