We present first results from a program of Atacama Large Millimeter/submillimeter Array ( ALMA ) CO ( 2–1 ) observations of circumnuclear gas disks in early-type galaxies . The program was designed with the goal of detecting gas within the gravitational sphere of influence of the central black holes . In NGC 1332 , the 0 \farcs 3-resolution ALMA data reveal CO emission from the highly inclined ( i \approx 83 \arcdeg ) circumnuclear disk , spatially coincident with the dust disk seen in Hubble Space Telescope images . The disk exhibits a central upturn in maximum line-of-sight velocity reaching \pm 500 km s ^ { -1 } relative to the systemic velocity , consistent with the expected signature of rapid rotation around a supermassive black hole . Rotational broadening and beam smearing produce complex and asymmetric line profiles near the disk center . We constructed dynamical models for the rotating disk and fitted the modeled CO line profiles directly to the ALMA data cube . Degeneracy between rotation and turbulent velocity dispersion in the inner disk precludes the derivation of strong constraints on the black hole mass , but model fits allowing for a plausible range in the magnitude of the turbulent dispersion imply a central mass in the range \sim ( 4 - 8 ) \times 10 ^ { 8 } { M } _ { \odot } . We argue that gas-kinematic observations resolving the black hole ’ s projected radius of influence along the disk ’ s minor axis will have the capability to yield black hole mass measurements that are largely insensitive to systematic uncertainties in turbulence or in the stellar mass profile . For highly inclined disks , this is a much more stringent requirement than the usual sphere-of-influence criterion .