The Burst and Transient Source Experiment (BATSE) on the Compton Gamma Ray Observatory (CGRO) has triggered on 1122 cosmic gamma-ray bursts between 1991 April 19 and 1994 September 19. These events constitute the Third BATSE (3B) burst catalog. This catalog includes the events previously reported in the 2B catalog, which covered the time interval 1991 April 19 to 1993 March 9. We present tables of the burst occurrence times, locations, peak fluxes, fluences, and durations. In general, results from previous BATSE catalogs are confirmed here with greater statistical significance. The angular distribution is consistent with isotropy. The mean galactic dipole and quadrupole moments are within 0.6 σ and 0.3 σ, respectively, of the values expected for isotropy. The intensity distribution is not consistent with a homogeneous distribution of burst sources, with <V/V_max_ >= 0.33 +/- 0.01. The duration distribution (T_90_) exhibits bimodality, with peaks at ~0.5 and ~30 s. There is no compelling evidence for burst repetition, but only weak limits can be placed on the repetition rate.