We report the results of deep (4.6 hr) H-band spectroscopy of the well studied z ~ 12 H-band dropout galaxy candidate UDFj-39546284 with MOSFIRE on Keck-I. These data reach a sensitivity of 5-10 × 10^(–19) erg s^(–1) cm^(–2) per 4.4 Å resolution element between sky lines. Previous papers have argued that this source could either be a large equivalent width line emitting galaxy at 2 < z < 3.5 or a luminous galaxy at z ~ 12. We find a 2.2σ peak associated with a line candidate in deep Hubble Space Telescope Wide-Field Camera 3 Infrared grism observations, but at a lower flux than expected. After considering several possibilities, we conclude these data cannot conclusively confirm or reject the previous line detection, and significantly deeper spectroscopic observations are required. We also search for low-redshift emission lines in 10 other 7 < z < 10 z, Y, and J-dropout candidates in our mask and find no significant detections.