This is a question that depends on state law, but I believe that most states will permit differential voting in nonprofits if included in the bylaws. There can be many circumstances in which it would be appropriate, and I think you have suggested one of them. It makes sense to me that the board chair, who one might think has broader knowledge of the organization and more responsibility for it than any other director, would have the power to break a tie vote. This is certainly better than providing that the chair can vote only in the event of the tie, because that provision prevents the chair from creating a tie and thus defeating a motion that would otherwise pass by a single vote because the chair is disenfranchised and can’t vote on the question. 

Differential voting could also be applicable in a trade association where certain directors represent members who pay more dues because of the size of their budgets, or in a national organization where directors are elected by local chapters, some of which have many more individual members than others.  In a supporting organization, the supported charity may have representatives with more votes than the others to assure the supported organization’s ultimate control.  Nobody “owns” a charity, but people do control it. Those power relationships should be spelled out in the bylaws.  (See Ready Reference Page: “Bylaws Function as ‘Constitution’ of Nonprofit Corporations”)