(verb) -- To quietly laugh out loud. It is most often used in places where one would need to be quiet or discreet about using online chat programs.
AndrewF: "I had your mom last night."
AndrewF: "Dude, we're in class. You can't 'LOL'."
AndrewE: "I just did."
AndrewF: "At least do it quietly."
AndrewE: "How so?"
AndrewF: "Maybe qLOL?"