How do I reconnect a ceiling fan light chain?
If the chain is broken inside the housing where you can't see it, you will have to disassemble the lower light cover on the fan if so equipped(usually 3 small screws). Definitely turn off the power to the fixture and always double check with a voltage tester to confirm power is off. It is not uncommon for the chain to break or actually pull out of the switch assembly. Until you determine the extent of the problem, you can't plan the fix. If the chain is broken at a ball link, a simple snap link my solve your problem.  If it is pulled completely out of the pull switch, then you will have to remove the wire nuts and switch and get a replacement, usually available at any hardware store.  Reassemble, carefully tighten the new wire nuts, a safety wrap of electrical tape around the wire nuts and put cover back on.  It is actually a very simple fix if you have any experience with electrical repairs.  CAVEAT.  Be sure power is off before working with any wires.  Good luck.