There is a distinction to be made between the individual (i.e. the person who has been elected as the chair of the council for the year) and the function of chair (i.e. whoever happens to be in the hotseat at any particular meeting). With the current or outgoing chair in the hotseat, they can elect you as the new chair, record the fact that you're not there, appoint one of their number to take the chair to elect the vice chair (and it would be sensible to allow the outgoing chair to do this), then the successful candidate can take the chair for the remainder of the meeting, as any vice chair should if the chair is not present.