Does anyone know how critical it is to ground a ceiling fan? Is it OK to two wire it from a swag chain? Or will this electrocute someone?

The third ground wire provides an important safety feature on anything with a metal housing. That way if any of the hot wires short to the housing, it immediately blows the breaker of fuse. Common lamps somehow seem to escape the grounding requirements. You could do it, but at times, things do go wrong, and people do get killed.

A few years ago while I was in the middle of eliminating all the old 2 prong outlets in our church, somebody in the area did get killed due to a lack of a proper third prong. It is not worth the risk.

My Hampton Bay fan is out of balance. How do you realign the plades to stop the shaking. Bill