Locate your junction or fuse box, and switch off the circuit breaker or pull out the fuse for the electrical line to your ceiling fan.
Unscrew all bulbs and remove ornamental coverings from the light box, which houses the entire lighting assembly.
Find the three fasteners connecting the light box to the ceiling fan. Remove the screws, and remove the light box from fan. Use a touch-type voltage tester to make sure the power is cut by touching the tester directly to an empty light socket or one of the connecting wires now visible from the fan.
Take off the end cap, which can be identified as the circular section that the pull chain hangs out of, by unscrewing it counterclockwise, and pull it off over the pull chain. This gives access to all connective wires.
Disconnect the wires, and remove the pull chain.
Insert the new pull chain switch. Screw the end cap back onto the light box so that it keeps the pull chain switch from falling out. You should still be able to access the wires from the rear of the light box.
Connect a black wire from the pull chain switch to a black wire from light box. Either one is fine. Connect the other switch wire to the remaining black wire that was connected to the old switch. Put electrician's tape around the connectors where they meet the wire.
Press all wires into the fan box, and reattach the light to the fan with the three screws.
Replace all lights and ornamental coverings onto your Hunter ceiling fan, and turn circuit breaker back on to test the new pull chain switch.