A: I want to be very careful not to mislead you. My reason for this care is that the situation you describe is very unusual and you may actually be mistaken about the requirement.

It is unusual for an organization not to allow its chairman to vote. It is, however, common practice to disallow his voting unless his vote effects the outcome. For instance, if a majority vote is required and the vote is tied (and thus the motion would fail), the chairman could vote in the affirmative, breaking the tie, causing the vote to pass; or, if there is one more vote in the affirmative than the negative (and thus the motion would pass), the chairman could vote in the negative, creating a tie, causing the vote to fail.

In general, non-voting members should not be considered in determining a quorum.

My suggestion is that you check your organization's bylaws to determine if they actually do state that the Chairman may not vote.

See RONR p. 339; Parliamentary Law, Question #287.