It can be done no problem. How it is done depends on how the existing wiring is connectred and routed. If you are just intending to add a new cable for the second fixture then just install a wire over the wires at the old fixture location and put a blank cover plate on the box. You can not hide the box in the ceiling.

I'll try to diagram this as I don't think I was clear. This is how it is now:

Chain Operated Switch Operated

Light Light

/ /

/ /

/ /

Hot Wire From Switch

This is how I want it (assume that the two fixtures will be represented by new flourescent lights):

Chain Operated Switch Operated

Light Light

\ /

\ /

\ /

From Switch

What happens to the "hot wire" that was not attached to the switch? Can I put those plastic electrical nuts on the ends or do I have to disconnect it at the source? Thanks.

Please ignore the last diagram as the formatting didn't work.

This is how it is.

Chain Light

from

Hot wire

Other Light

from

switch

This is how I want it.

Both lights from switch

What do I do with the hot wire from the original chain light so that I don't start a fire?

If you can kill the circuit that would be best. Especially if this is a constant or unswitched hot. This would avoid any confusion in the future. In the event you do not want to kill the power, you can cap it off with a wire nut but tag the wire as a constant hot.

I would keep the constant hot wire and use it for an emergency ballast. This way if yoour power goes out the emergency ballast would kick in and provide light for about 1.5 hours. The emergency ballast needs an unswitched power supply to function properly. After you run the switched power from the other light you will have a perfect setup for this.

U.S.M.C. Semper Fi !!!