The observation by the BATSE instrument on the Compton Gamma Ray Observatory that gamma-ray bursts (GRBs) are distributed isotropically around Earth but nonuniformly in distance has led to the widespread conclusion that GRBs are most likely to be at cosmological distances, making them the most luminous sources known in the universe. If bursts arise from events that occur in normal galaxies, such as neutron star binary inspirals, then they will also occur in our Galaxy about every 10(5)-10(6) years. The gamma-ray flux at Earth due to a Galactic GRB would far exceed that from even the largest solar flares. The absorption of this radiation in the atmosphere would substantially increase the stratospheric nitric oxide concentration through photodissociation of N-2, greatly reducing the ozone concentration for several years through NOx catalysis, with important biospheric effects due to increased solar ultraviolet flax. A nearby GRB may also leave traces in anomalous radionuclide abundances.