Air Conditioning Stops Functioning When Headlights in Use

I have a 2002 Chrysler Sebring Limited Convertible. If I turn on the headlights, the air conditioning stops working, and warm air starts streaming out of the front defroster. The dash for the climate control knobs is not backlit when I turn on the headlights. This has been going on for a few months, and I have not noticed any other symptoms. I'm in Georgia, so the nights are still toasty warm, and I'd like to figure out what's going on.