We have obtained optical long-slit spectroscopy of the nucleus of M32 using the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope. The stellar rotation velocity and velocity dispersion, as well as the full line-of-sight velocity distribution (LOSVD), were determined as a function of position along the slit using two independent spectral deconvolution algorithms. We see three clear kinematical signatures of the nuclear black hole: a sudden upturn, at ∼ 0.3 ′ ′ from the center, in the stellar velocity dispersions; a flat or rising rotation curve into the center; and strong, non-Gaussian wings on the central LOSVD. The central velocity dispersion is ∼ 130 km s −1 (Gaussian fit) or> ∼ 175 km s −1 (corrected for the wings). Both the velocity dispersion spike and the shape of the central LOSVD are consistent with the presence of a supermassive compact object in M32 with a mass in the range 2 − 5 × 10 6 M⊙. These data are a significant improvement on previous stellar kinematical data
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