We report the redshift measurement for the submillimeter selected galaxy SMM J04431+0210 ( N4 ) using the Near Infrared Spectrograph on the Keck II telescope . The data show H \alpha , [ NII ] 6583,6548 , and [ OIII ] 5007 lines at a redshift of z = 2.51 . The high nuclear [ NII ] /H \alpha line ratio is consistent with a LINER or Type-II AGN . The H \alpha emission is spatially resolved , suggesting the presence of significant star-forming activity outside the nucleus . From imaging with the Near Infrared Camera on the Keck I telescope , we find an extremely red near-infrared color of J - K=3.2 for N4 . Follow-up redshifted CO ( 3 \rightarrow 2 ) observations with the Owens Valley Millimeter Array constrain the mass of molecular gas to be less than 4 \times 10 ^ { 10 } M _ { \odot } , after correcting for lensing . The CO to sub-mm flux limit , the spectroscopic line ratios , and the spectral energy distribution for N4 are all within the range of properties found in other high-redshift sub-mm sources and local ultraluminous infrared galaxies . After the correction for lensing , N4 is the weakest intrinsic sub-mm selected source with a known redshift and represents the first redshift for the < 2 mJy 850 \mu m sources which are responsible for the bulk of the emission from the sub-mm population as a whole . We argue that N4 contains either an AGN or LINER nucleus surrounded by an extended region of active star-formation .