Kitchen light worked for a few hours then stopped. Now it won't turn on. I tested it with meter and there was power in the switch in off position. Every thing else connected to circuit still works.

"I tested it with meter and there was power in the switch in off position". IN the switch, AT the switch or THROUGH the switch? There should be power on one side of a switch in the OFF position. Have you checked the bulb or for a loose wire connection?

There should be power at the stitch in the off position. But test it with the switch turned on. You didn't say which type of light it is. In a working circuit, when the switch is closed there won't be any power read at the switch. Is this a incandescent, a cfl, a fluorescent with a ballast? The first thing to do is usually the simplest... such as change the bulb.