We report ~1" resolution K-band (2 micron) imaging spectroscopy of the central parsec of our Galaxy. The derived radial velocities for 223 early and late type stars probe thenuclear mass distribution to spatial scales of 0.1 pc. We find a statistically very significant increase of projected stellar velocity dispersion from about 55 km/s at p~5 pc to 180 km/s at p~0.1 pc. The stars are also rotating about the dynamic center. The late type stars follow general Galactic rotation, while the early type stars show counter- rotation. Fitting simultaneously the observed projected surface densities and velocity dispersions we derive the intrinsic volume densities and radial velocity dispersion as a function of distance from the dynamic center for both types of stars. We then derive the mass distribution between 0.1 and 5 pc from the Jeans equation assuming an isotropic velocity field. Our analysis requires a compact central dark mass of 2.5 to 3.2*10^6, at 6 to 8 sigma significance. The dark mass has a density of 10^9 M_o pc^-3 or greater and a mass to 2 micron luminosity of >=100. The increase in mass to luminosity ratio can be reduced but not eliminated even if extreme anisotropic velocity distributions are considered. The dark mass cannot be a cluster of solar mass remnants (such as neutron stars). It is either a compact cluster of 10-20 M_o black holes or a single massive black hole.