Short for "Que La Chinga". In Spanish, "Que" = What, "La" = The, and "Chinga" = Fuck. QLC is like WTF, literally translated in Spanish. In Spanish, the phrase "Que La Chinga" actually doesn't mean anything, but it's good to use in situations where you can't say "What The Fuck" or "WTF", like at work for example.
QLC man, the store closed like a hour ago and that customer's still in here, I wanna get the fuck outta here.