Turn the ceiling fan off at the light switch.
Follow the chain pull from the bottom until you reach the joining bead.
Pull the top bead in bottom half of the chain up from the bottom of the joint bead to the center.
Pull the top bead in the bottom half of the chain through the center of the joint bead.
Put the last bead in the new chain into the center of the joint bead and slide it down to the bottom until it clicks into place.