The Hanover Country Club would seem to be Dartmouth’s oldest athletic building, a nineteenth-century barn remodeled as an Arts & Crafts clubhouse by Homer Eaton Keyes in 1916. It is still in excellent shape and well used, although there has been talk for several years of replacing it, presumably with a clubhouse some distance from campus on Lyme Road.
(The school’s oldest intercollegiate athletic facility must be the Alumni Oval of 1893, which was remodeled as Memorial Field and is being remodeled again this summer — meaning that the site and the form have been replicated through the years but that none of the original materials survive.)
[Update 09.12.2006: clubhouse remodeling date corrected.]