Assuming you actually mean the Nunchuck and not the Wiimote, it could be as simple as bad wiring. The Nunchuck wires into the Wiimote which communicates with the system so there should be no real problem with Nunchuck communicating with the console except with the remote itself. Are you sure that the Wiimote is not to blame? Again, I can only think of bad wiring or bad plug/port.