  We present Atacama Large Millimeter/submillimeter Array (ALMA) Cycle 3
observations of CO(2-1) emission from the circumnuclear disk in the E/S0 galaxy
NGC 1332 at 0.044" resolution. The disk exhibits regular rotational kinematics
and central high-velocity emission (+/-500 km/s) consistent with the presence
of a compact central mass. We construct models for a thin, dynamically cold
disk in the gravitational potential of the host galaxy and black hole, and fit
the beam-smeared model line profiles directly to the ALMA data cube. Model fits
successfully reproduce the disk kinematics out to r=200 pc. Fitting models just
to spatial pixels within projected r=50 pc of the nucleus (two times larger
than the black hole's gravitational radius of influence), we find
M_BH=6.64(-0.63,+0.65)*10^8 solar masses. This observation demonstrates ALMA's
powerful capability to determine the masses of supermassive black holes by
resolving gas kinematics on small angular scales in galaxy nuclei.
