  We present a new stellar dynamical mass measurement of the black hole in the
nearby, S0 galaxy NGC 3998. By combining laser guide star adaptive optics
observations obtained with the OH-Suppressing Infrared Imaging Spectrograph on
the Keck II telescope with long-slit spectroscopy from the Hubble Space
Telescope and the Keck I telescope, we map out the stellar kinematics on both
small spatial scales, well within the black hole sphere of influence, and on
large scales. We find that the galaxy is rapidly rotating and exhibits a sharp
central peak in the velocity dispersion. Using the kinematics and the stellar
luminosity density derived from imaging observations, we construct
three-integral, orbit-based, triaxial stellar dynamical models. We find the
black hole has a mass of M_BH = (8.1_{-1.9}^{+2.0}) x 10^8 M_sun, with an
I-band stellar mass-to-light ratio of M/L = 5.0_{-0.4}^{+0.3} M_sun/L_sun
(3-sigma uncertainties), and that the intrinsic shape of the galaxy is very
round, but oblate. With the work presented here, NGC 3998 is now one of a very
small number of galaxies for which both stellar and gas dynamical modeling have
been used to measure the mass of the black hole. The stellar dynamical mass is
nearly a factor of four larger than the previous gas dynamical black hole mass
measurement. Given that this cross-check has so far only been attempted on a
few galaxies with mixed results, carrying out similar studies in other objects
is essential for quantifying the magnitude and distribution of the cosmic
scatter in the black hole mass - host galaxy relations.
