Disconnect the electricity to the pull chain light fixture at the main breaker panel. Locate the breaker that supplies electricity to the light fixture and turn it off.
Remove the light shade and the light bulbs if applicable. Remove the screws to the light fixture holding it to the ceiling electrical box.
Pull the fixture from the ceiling and untwist the wire connectors holding the white wire from the light fixture and the white wire from the ceiling electrical box together. Untwist the connector holding the two black wires together, the one from the ceiling box and one from the light fixture pull chain switch. Finish disconnecting the light fixture from the ceiling by untwisting the connector holding the bare copper wire from the ceiling electrical box to the green ground wire from the light fixture.
Move your light fixture to a sturdy work surface. Untwist the retaining nut from the exterior of the light fixture that holds the pull chain switch. The chain from the switch threads through the retaining nut for easy identification.
Untwist the connector holding a black wire from the pull chain switch to the black wire from the light fixture. The pull chain switch has two black wires attached to it. One wire connects to the power supply wire inside the electrical box and the other wire connects to the light fixture.
Remove the old pull chain switch from the light fixture and discard it. Insert the threaded throat of a replacement pull chain switch through the opening you removed the old switch from. Thread the chain through the retaining nut and attach the nut to the threaded throat of the switch, turning it clockwise.
Connect the black wire from the light fixture to a black wire from the pull chain switch by twisting an orange wire connector onto both wires.
Twist an orange wire connector to the black wire from the ceiling electrical box to the remaining black wire of the pull chain switch, connecting them together. Reconnect the two white wires together with another orange wire connector. Twist an orange wire connector onto the bare copper wire from the ceiling electrical box connecting it with the green wire from the light fixture.
Reattach the light fixture to the ceiling electrical box with the screws you removed in Step 2. Replace the light bulbs and the light shade onto the light fixture. Turn the electricity on at the main electrical breaker panel.