We present improved spectroscopy of M32 with the Canada-France-Hawaii Telescope and Subarcsecond Imaging Spectrograph. Tip-tilt guiding provides a resolution of FWHM ϭ 0"47 or * ϭ 0"20 ( * ϭ Gaussian dispersion radius of the point-spread function). The observed central velocity dispersion, 3 92 H 5 km s Ϫ1 , and the maximum rotation velocity, V max ϭ 55 H 3 km s Ϫ1 , are larger than at lower resolution. In addition, the measured line-of-sight velocity distributions indicate the possible presence of broad wings at radii r = 0"2, with significant numbers of stars at ⌬V 3 200 km s Ϫ1 from the mean velocity. Two-integral dynamical models fit these data provided that M32 contains a central dark object, probably a black hole, of mass M q 3 (3.0 H 0.5) ϫ 10 6 M J . This confirms detections based on lower resolution spectra by Tonry, Dressler, Richstone, van der Marel, Dehnen, and collaborators. The available spatial resolution has now improved by a factor of 3 since Tonry's discovery observations; each improvement in resolution has strengthened the case for a black hole in M32.