The BATSE observations (Fishman et al.; Meegan et al.) show that the angular distribution of gamma-ray sources in the sky is isotropic. These observations are shown to be consistent with a cosmological distribution of sources. In fact, the observed distribution of V/Vmax values is the one toward which a cosmological distribution converges. If there is even a weak cosmological time dependence of the event rate, then the bursts originate at modest z values. For flat cosmological models, this requires 10 exp 50 ergs or less. The energy and the observed event rate are in full agreement with the binary neutron star merger model.