If you are not sure that your nunchuck is original, then it's not. I had a Nintendo branded Wiimote+Nunchuck but it was not original, once you see an original one you can see small but important differences, especially in the connectors. My nunchuck also died and I bought an original one which I'm sure will last much more than my old one.
Rig
*Corei5 3570K *Nvidia 9800GT 1GB DDR3
*Motherboard Asus P8H77M-PRO *Win7 x64
*RAM 8GB DDR3(1600)
