Light curves of the W Ursae Majoris binary AH Cancri obtained in 1973 and 1988 show a remarkable change in shape. Earlier curves have rounded minima and eclipses appear to be partial; later curves have flat-bottomed minima indicating total eclipses. The 1973 curves are consistent with a system in overcontact with an orbital inclination of approximately 65°. Such a low inclination, however, is incompatible with the -duration flat-bottomed eclipse seen in the more recent light curves. Intrigued by this puzzle we decided to make new photometric observations. We present CCD photometry in V and R obtained with the Southeastern Association for Research in Astronomy (SARA) 0.9-m and Buehler Observatory 0.4-m telescopes. We solve the new light curves and find a high-inclination (i ≈ 84°), low-mass-ratio (q ≈ 0.145) model fits the observations reasonably well. In the post-1988 light curves, limb darkening causes eclipses of the cooler star to be deeper than those of the hotter star. Times of minima suggest a possible third body interaction.