The chickens are supposed to sit down whilst they incubate an egg. Sometimes, they don't. They just keep on walking around - the egg still incubates though. Heaven knows where they keep that egg as they strut about the place!
Animal Sciences did some research on the Chickens in our game and referred them to the Chicken Psychology Department. After some discussion with our NPC Chickens, we believe they should stay put now, if you see something odd about this, please let us know. :)