Whether siding with the drow is chaotic, lawful or neutral evil depends on your reaction to the ever seeing eye and the conversation from the guards to the worg pens. If you know that the real power lies in moonrise towers than finding your way to into the bottom rung of the hierarchy and working your way up is just what a lawful evil person does.
So it can be chaotic "I want blood and fire" but I can be lawful or neutral "I see opportunity here".
