We report ̃1" resolution K-band (2 μm) imaging spectroscopy of the central parsec of our Galaxy. The derived radial velocities for 223 early- and late-type stars probe the nuclear 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-1 at p ̃5 pc to 180 km s-1 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 dispersions 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 2.5-3.2 x 106 Msun, at 6-8 σ significance. The dark mass has a density of 109 Msun pc-3 or greater and a mass to 2 μm 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 Msun black holes or a single massive black hole.