I work as a auto tech, and have seen this before on several GM vehicles. Apparently, their is a problem with the wiring harness/pigtail connector. The fix is to cut the pigtail at the headlight connector, and crimp in a new UPDATED connector available only at GM dealerships.
It should come with an instruction sheet and a few weather-tite connectors.
Their are 2 black wires that need to be connected together, so be sure to read before you crimp. Best way to do it is to just twist the wires together as per the instruction sheet, and then test headlight operation. If it works, you got the wiring right. Make sure to test hi-beam operation as well.
If all is good, disassemble, and then crimp. Then do the same for the other side.
Hope that helps out.