Unplug the headlight and check for power at the plug with the lowbeam switch on. The ground must be good because the Highbeam uses the same ground. If there's no power, see if you can trace the wire back. I'm almost positive that on Chevys, the power runs straight to one headlight then bridged to the other headlight. Let us know what you find. Good luck!
I was trying to look for some schematics on your vehicle, but while searching I may have come across a similar setup. Some have the headlights wired throught the dimmer switch, so just verify your dimmer switch/dome light works. Not trying to have you replace parts unless you know for a fact they're bad.