According to Board of Trustees bylaws, do not use chairman or chairwoman unless referring to named professorships that use those words. Instead, use chair. For those outside the university, use their official title, either chair or chairman/chairwoman.
Across WashU schools, chair is preferred for leaders of departments. Do not use chairman or chairwoman. At WashU Medicine, director is used for people who head divisions (though there are some division leaders who use chief); chief is used for people who lead sections.
Capitalize chair when directly preceding name, but lowercase in other usages.