How can I fix this chandelier socket?
This is a relatively easy DIY job.  The sockets are most of the time removable.  I can't tell exactly from your picture, but they are usually held in place by a screw below, the socket itself screws in, or the sockets sometimes have a thread on the top and a bolt holds it down.  Remove the reflector/glass and take a look to see if you can figure out how to remove it.  There will be two wires attached, usually with a screw terminal.  Unscrew the wires and remove the socket.  Go to Home Depot or your local hardware store and find an exact replacement (they are 99% of the time standard sockets).  Re-attach the wires (doesn't matter if they are reversed in this case), re-attach the socket and enjoy your handy work!