How do I repair an on/off chain that has broken off on a Hampton Bay fan ?

Just had to do it myself. Undo section were chain was and get to wiring. You have to take the part off that has the chain and go to Lowe's, home depot etc. with the part and get a new part. Very easy to change out. Once power is off you get wires out of broken one by sticking a paperclip in where the wire are pushed in and just pull the wire out and take the part to get a replacement.
All that part was very easy but the hardest part was putting all the wiring back in and putting the cap back on. We had a light on our fan though.

Follow these instructions here:

Ceiling fan pull chain replacement and repair - Ceiling Fans N More