Chickens make a lot of different vocalizations, some sound very similar but have different meanings. One I've noticed that sounds very close to the "egg song" is one I've heard when they are nervous. It's like they feel like something is wrong or threatening but aren't sure what.
Then what does the "egg song" actually mean. Just by what people call it, some people think it is a hen bragging about laying an egg. I don't think it has anything to do with an egg. I think it is a location call. The flock has moved while the hen was laying the egg. When she comes off the nest she calls out "Hey, where are you?" Sometimes, not always but sometimes, my rooster will go find her and lead her back to the flock. After mating her, of course. If she is laying eggs those eggs need to be fertile. Sometimes when a chicken is separated from the flock it might call out to try to find them.
I could be totally wrong about what that sound actually means. But I do not find it strange that a chick will speak "chicken" even at that age. I just may not interpret it correctly, whatever it is saying.
