The PC (and most instrumentation) chassis are both, almost always, connected to earth ground.
I agree that connecting it to the neutral wire in a household wiring system could be dangerous, albeit rare and unlikely to cause a problem, but an earth ground should be fine. It's the way almost all of the ESD mats I've used have been connected, and the only line in a mains system guaranteed to always be connected to earth (literally, the Earth).
You could go out of your way to connect it to another, separate earth ground, such as a cold water pipe or a new embedded copper grounding rod, but I think that would be a bit of overkill.