We extract the shape of the stellar velocity ellipsoid as a function of radius in M87 from van der Marel's [MNRAS, 270, 271 (1994)] velocity dispersion data. We include the gravitational force of a central black hole with the mass quoted by Harms et al. [ApJ, 435, L35 (1994)]. The kinematical data are corrected for the effects of seeing and instrumental blurring using a nonparametric algorithm. We find that the stellar motions in M87 are slightly radially anisotropic throughout the main body of the galaxy, with sigma(r) approximate to 1.2 sigma(t). However, sigma(t) exceeds sigma(r) within the inner 1'' - 2'' by a statistically significant amount. A number of models for the formation of nuclear black holes predict a tangential anisotropy in the stellar motions, and our results provide evidence for such an effect in M87. (C) 1997 American Astronomical Society.