The Third EGRET Catalog of High-Energy Gamma-Ray Sources is based on data obtained by the Energetic Gamma-Ray Experiment Telescope (EGRET) on board the Compton Gamma-Ray Observatory (CGRO) during the period from 1991 April 22 to 1995 October 3, corresponding to GRO Cycles 1, 2, 3, and 4. EGRET is sensitive to photons in the energy range from about 30 MeV to over 20 GeV, the highest energies accessible by the CGRO instruments, and, like COMPTEL, is an imaging instrument. In addition to including more data than the Second EGRET Catalog (2EG, Thompson et al. 1995, ApJS, 101, 259) and its supplement (2EGS, Thompson et al. 1996, ApJS, 107, 227), this catalog uses completely reprocessed data so as to correct a number of mostly minimal errors and problems. The 271 sources (E > 100 MeV) in the catalog include the single 1991 solar flare that was bright enough to detected as a source, the LMC, 5 pulsars, one probable radio galaxy detection (Cen A), and 66 high-confidence identifications of blazars (BL Lac objects, flat-spectrum radio quasars, or unidentified flat-spectrum radio sources). In addition, 27 lower-confidence potential blazar identifications are noted. Finally, the catalog contains 170 sources that are not yet firmly identified with known objects, although potential identifications have been suggested for a number of these. As already noted, there are 271 distinct sources in this catalog: since there are multiple measurements for these sources corresponding to the various viewing periods, there are 5246 entries in the HEASARC's version of the 3rd EGRET Catalog corresponding to the same number of lines in Table 4 of the published version. Thus, there are an average of about 20 entries for every distinct source. Notice that 14 sources reported in the 2nd EGRET Catalog or its supplement do not appear in this 3rd EGRET Catalog: 2EG J0403+3357, 2EG J0426+6618, 2EGS J0500+5902, 2EGS J0552-1026, 2EG J1136-0414, 2EGS J1236-0416, 2EG J1239+0441, 2EG J1314+5151, 2EG J1430+5356, 2EG J1443-6040, 2EG J1631-2845, 2EG J1709-0350, 2EG J1815+2950, and 2EG J2027+1054 due to the fact that the re-analysis of the EGRET data has dropped their statistical significance from just above the catalog threshold to just below it; additional information on these sources is provided in Table 5 of the published version of the 3rd EGRET Catalog. This database table was created by the HEASARC in June 1999, based on a machine-readable version of Table 4 of the 3rd EGRET Source Catalog that was provided by the CGRO Science Support Center (CGROSSC). Slight modifications to the Browse Object Classifications were later made in April 2001. This is a service provided by NASA HEASARC .