We carried out targeted ALMA observations of 129 fields in the COSMOS region at 1.25 mm , detecting 152 galaxies at S/N \geq 5 with an average continuum RMS of 150 \mu Jy . These fields represent a S/N-limited sample of AzTEC / ASTE sources with 1.1 mm S/N \geq 4 over an area of 0.72 square degrees . Given ALMA ’ s fine resolution and the exceptional spectroscopic and multiwavelength photometric data available in COSMOS , this survey allows us unprecedented power in identifying submillimeter galaxy counterparts and determining their redshifts through spectroscopic or photometric means . In addition to 30 sources with prior spectroscopic redshifts , we identified redshifts for 113 galaxies through photometric methods and an additional nine sources with lower limits , which allowed a statistically robust determination of the redshift distribution . We have resolved 33 AzTEC sources into multi-component systems and our redshifts suggest that nine are likely to be physically associated . Our overall redshift distribution peaks at z \sim 2.0 with a high-redshift tail skewing the median redshift to \tilde { z } =2.48 \pm 0.05 . We find that brighter millimeter sources are preferentially found at higher redshifts . Our faintest sources , with S _ { 1.25 mm } ¡1.25 mJy , have a median redshift of \tilde { z } =2.18 \pm 0.09 , while the brightest sources , S _ { 1.25 mm } ¿1.8 mJy , have a median redshift of \tilde { z } =3.08 \pm 0.17 . After accounting for spectral energy distribution shape and selection effects , these results are consistent with several previous submillimeter galaxy surveys , and moreover , support the conclusion that the submillimeter galaxy redshift distribution is sensitive to survey depth .