THE nature of the sources of cosmic γ-ray bursts is a long-standing problem in astrophysics. Lack of knowledge of their true spatial distribution and of their intrinsic brightness has hampered theoretical understanding of these enigmatic events. The Burst and Transient Source Experiment on the Compton Gamma-Ray Observatory has been detecting bursts at the rate of about one a day, and we report here an analysis of 153 events. The number versus intensity distribution does not follow the -3/2 power law expected for a spatially extended homogeneous distribution of sources, but at the same time the angular distribution is isotropic within statistical limits. Taken together, these results are inconsistent with the spatial distribution of any known population of galactic objects, but may be consistent with the bursts being at cosmological distances.