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 holes gravitational radius of influence), we find M_BH=6.64(-0.63,+0.65)*10^8 solar masses. This observation demonstrates ALMAs powerful capability to determine the masses of supermassive black holes by resolving gas kinematics on small angular scales in galaxy nuclei.
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