Good post; I have less experience (maybe 6 or 7 boards) but I'll slightly disagree about scope of the role.
Sometimes the Chair can get too involved and sway the direction of the company, without the rest of the board having much say in the matter. I'm guessing a number of us in the AVC community have witnessed this (or participated).
Distinguishing between the will of the Board and the will of the Chair becomes difficult for the CEO if the Chair goes beyond that.
The primary role of Chair is to open, moderate, and close the meetings, set dates for next meetings, and then anything conferred to her by the will of the board (note I said her--however completely unlikely that is given our still rather biased board-selection tendencies that lead to male-heavy boards ..cough cough, Facebook).
Anything beyond that is outside the Chair's authority.
Power, however, is what you get people to do because of your authority, which a lot of board members (and Chairs) take advantage of.
On the flip side, if the Chair doesn't set dates, doesn't moderate well, doesn't keep the CEO aware of the Board's directives, expectations can easily be missed and board members can feel dissatisfied.
It's really up to the CEO to make sure communication is flowing and the company is aligned with the will of the board, because ultimately it's her job on the line and the Chair is just one of several/many vote(s).