  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.
