The 18,806 ROSAT All Sky Survey Bright Source Catalog (RASS/BSC) X-ray sources are quantitatively cross-associated with near-infrared (NIR) sources from the Two Micron All Sky Survey Point Source Catalog (2MASS/PSC). An association catalog is presented, listing the most likely counterpart for each RASS/BSC source, the probability P_id (called id_prob in the HEASARC version of this catalog) that the NIR source and X-ray source are uniquely associated, and the probability P_no-id (called no_id_prob in the HEASARC version of this catalog) that none of the 2MASS/PSC sources are associated with the X-ray source. The catalog includes 3853 high quality (P_id>0.98) X-ray-NIR matches, 2280 medium quality (0.98 >= P_id > 0.9) matches, and 4153 low quality (0.9 >= P_id > 0.5) matches. Of the high quality matches, 1418 are associations that are not listed in the SIMBAD database, and for which no high quality match with a USNO-A2 optical source was presented for the RASS/BSC source in previous work (Rutledge et al. 2000, ApJS, 131, 335). The present work offers a significant number of new associations with RASS/BSC objects that will require optical/NIR spectroscopy for classification. For example, of the 6133 P_id > 0.9 2MASS/PSC counterparts presented in the association catalog, 2411 have no classification listed in the SIMBAD database. These 2MASS/PSC sources will likely include scientifically useful examples of known source classes of X-ray emitters (white dwarfs, coronally active stars, active galactic nuclei), but they may also contain previously unknown source classes. It is determined that all coronally active stars in the RASS/BSC should have a counterpart in the 2MASS/PSC, and that the unique association of these RASS/BSC sources with their NIR counterparts thus is confusion limited. This table was created by the HEASARC in October 2009 based on an electronic version of Table 3 (the 'Association Catalog') from the paper which were obtained from the Astrophysical Journal web site. This is a service provided by NASA HEASARC .