The question itself is scientifically moot. It's not a question that can be answered. First off, what defines a chicken? What defines an egg? Is the ancestor of a chicken still considered a chicken? Is an egg that's not a chicken egg still an egg? An egg itself is the product of cell reproduction - is the cell then considered part of the egg? Where's the cutoff point? At one point can you say that a creature has fully evolved into a chicken? Sure, a chicken a million years ago won't be able to mate with a chicken today, but on the other hand, a chicken two hundred years ago probably would have the same problem.
And of course, the necessary set of genetic changes, if you could identify them, obviously didn't happen all at once. They occurred over a long period of time, probably in both egg and chicken stages. And to be honest, scientists are not entirely sure how genetic changes occur and prove beneficial. There are some sound theories, but we've hardly been aware of DNA long enough to observe the evolutionary process in a way that can provide substantiation. So perhaps genes are randomly mutated in the fertilization process or perhaps other causes turn on and off genetic switches. Perhaps all that area we've been referring to as "junk DNA" is significant. Perhaps there's a reason why a twin has a genetic disorder and another is healthy.
Point being, we know so little about DNA. What we do know is that it's not quite so simple as "chicken" and "not chicken."
In other words, a chicken does not get bit by a radioactive spider and the next generation is Spiderman.