The authors have quantitatively cross-associated the 18,811 ROSAT All-Sky Survey Bright Source Catalog (RASS/BSC) X-ray sources with optical sources in the USNO A-2 catalog, calculating the probability of unique association (P_id) between each candidate within 75" of the X-ray source position, on the basis of optical magnitude and proximity. They have generated catalogs of RASS/BSC sources for which P_id > 98%, P_id > 90%, and P_id > 50%, which contain 2705, 5492, and 11,301 unique USNO A-2 optical counterparts respectively down to the stated level of significance. Together with identifications of objects not cataloged in USNO A-2 due to their high surface brightness (M31, M32, ...) and optical pairs, they produced a total of 11,803 associations to a probability of P_id > 50%. They also include in this catalog a list of objects in the SIMBAD database within 10" of the USNO A-2 position, as an aid to identification and source classification. This is the first RASS/BSC counterpart catalog which provides a probability of association between each X-ray source and counterpart, quantifying the certainty of each individual association. The catalog is more useful than previous catalogs which either rely on plausibility arguments for association or do not aid in selecting a counterpart between multiple off-band sources in the field. Sources of high probability of association can be separated out, to produce high-quality lists of classes (Seyfert 1/2s, QSOs, RS CVns) desired for targeted study, or for discovering new examples of known classes (or new classes altogether) through the spectroscopic classification of securely identified but unclassified USNO A-2 counterparts. Low P_id associations can be used for statistical studies and follow-on investigation - for example, performing follow-up spectroscopy of the many low-mass stars to search for signatures of coronal emission, or to investigate the relationship between X-ray emission and classes of sources not previously well-studied for their X-ray emissions (such as pulsating variable stars). The authors find that a fraction ~65.8% of RASS/BSC sources have an identifiable optical counterpart, down to the magnitude limit of the USNO A-2 catalog which could be identified by their spatial proximity and high optical brightness. This table was created by the HEASARC in October 2009 based on electronic versions of Tables 9 (USNO counterparts for which P_id > 98%) and 10 (USNO counterparts for which 90% > P_id > 98%) of the reference paper which were obtained from the Astrophysical Journal web site. This is a service provided by NASA HEASARC .