We present the stellar kinematics in the central 2 of the luminous elliptical galaxy M87 (NGC 4486), using laser adaptive optics to feed the Gemini telescope integral-field spectrograph, NIFS. The velocity dispersion rises to 480 km/s at 0.2. We combine these data with extensive stellar kinematics out to large radii to derive a black-hole mass equal to (6.6+-0.4)x10^9 Msun, using orbit-based axisymmetric models and including only the NIFS data in the central region. Including previously-reported ground-based data in the central region drops the uncertainty to 0.25x10^9 Msun with no change in the best-fit mass; however, we rely on the values derived from the NIFS-only data in the central region in order to limit systematic differences. The best-fit model shows a significant increase in the tangential velocity anisotropy of stars orbiting in the central region with decreasing radius; similar to that seen in the centers of other core galaxies. The black-hole mass is insensitive to the inclusion of a dark halo in the models --- the high angular-resolution provided by the adaptive optics breaks the degeneracy between black-hole mass and stellar mass-to-light ratio. The present black-hole mass is in excellent agreement with the Gebhardt & Thomas value, implying that the dark halo must be included when the kinematic influence of the black hole is poorly resolved. This degeneracy implies that the black-hole masses of luminous core galaxies, where this effect is important, may need to be re-evaluated. The present value exceeds the prediction of the black hole-dispersion and black hole-luminosity relations, both of which predict about 1x10^9 Msun for M87, by close to twice the intrinsic scatter in the relations. The high-end of the black hole correlations may be poorly determined at present.
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