Unfortunately, the only way to discharge it is to ground yourself. The only way to ground yourself is to touch grounded metal (I think that it has to be metal). So the only way to ground a metal computer case is to have the power supply attached to it with screws, and to have the power supply plugged into a grounded wall outlet. However, the power supply doesn't have to be on (it should actually be off anyway for maximum safety)
Worse yet, the discharge is usually not even felt; only the larger amounts are felt. Fortunately, it doesn't have to be felt for it to be effective.
So another way to ground yourself (to discharge any static electricity) is by touching one of the screws that are holding a light switch's face plate on the wall. Of course, that switch has to be connected to a grounded line in order for it to work. Fortunately, most are! Although, not all wall outlets are grounded. However, if you have one of those surge suppressors that has an LED to indicate whether or not it's grounded, then you can use it to test each outlet.
So I figure that it's best to take no chances. In fact, I even wear as little clothing as possible. If I'm alone, then this really does mean that I might take off my shirt and pants to avoid extra static build-up. I've also been told that it's better to work barefoot, but I don't know if this is true; except, I go barefoot anyway.
Regarding those chair mats: mine is often full of static, so I don't know how beneficial these are when trying to use them as a way to avoid static build-up. However, mine has no anti-static properties.