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We present first results from a program of Atacama LargeMillimeter/submillimeter Array (ALMA) CO(2-1) observations of circumnuclear gasdisks in early-type galaxies. The program was designed with the goal ofdetecting gas within the gravitational sphere of influence of the central blackholes. In NGC 1332, the 0.3"-resolution ALMA data reveal CO emission from thehighly inclined (i~ 83 degrees) circumnuclear disk, spatially coincident withthe dust disk seen in Hubble Space Telescope images. The disk exhibits acentral upturn in maximum line-of-sight velocity reaching +-500 km/s relativeto the systemic velocity, consistent with the expected signature of rapidrotation around a supermassive black hole. Rotational broadening and beamsmearing produce complex and asymmetric line profiles near the disk center. Weconstructed dynamical models for the rotating disk and fitted the modeled COline profiles directly to the ALMA data cube. Degeneracy between rotation andturbulent velocity dispersion in the inner disk precludes the derivation ofstrong constraints on the black hole mass, but model fits allowing for aplausible range in the magnitude of the turbulent dispersion imply a centralmass in the range ~(4-8)x10^8 Msun. We argue that gas-kinematic observationsresolving the black hole's projected radius of influence along the disk's minoraxis will have the capability to yield black hole mass measurements that arelargely insensitive to systematic uncertainties in turbulence or in the stellarmass profile. For highly inclined disks, this is a much more stringentrequirement than the usual sphere-of-influence criterion.

Toward Precision Black Hole Masses with ALMA: NGC 1332 as a Case Study in Molecular Disk Dynamics