It is possible to replace the broken pull chain on a ceiling fan. Replacement requires removing the old switch to attach a new chain from the hardware store. The replacement should be an exact match for the broken chain.
Before beginning work on fans or other electrical appliances, consumers should ensure the power is off to the device. Using a digital camera or cell phone to take a picture before removing any wires makes the replacement easier. If the switch itself is broken, SFGate recommends taking it to the store to ensure purchase of the correct replacement because these switches are not universal.