You can even charge while climbing, even though you move at half speed while doing it. Charging is pretty liberal in 4th Edition.
One rule I've heard thrown about but that I haven't actually seen written anywhere is that you have to be able to see the target of your charge when you start charging. I don't believe that's actually the case - for instance, I believe you can charge a drow that has dropped its cloud of darkness around itself or between you and it. Can anyone confirm one way or the other?
I would imagine you could charge a square, but take the appropriate negatives of attacking blindly... assuming the target is in the square (may have moved after dropping the cloud)...