We investigate the viability of Galactic corona models of gamma-ray bursts by calculating the spatial distribution expected for a population of high-velocity neutron stars born in the Galactic disk and moving in a gravitational potential that includes contributions from the bulge, disk, and dark matter halo of our Galaxy and also from these same components of our neighboring galaxy M31. We consider two classes of models: one in which the bursts radiate isotropically and one in which the bursts are beamed. We place constraints on these models by comparing the expected brightness and angular distributions with the data in the BATSE 3B catalog. We find that if the bursts radiate isotropically, then the Galactic corona model can reproduce the BATSE peak Bur and angular distributions for neutron star kick velocities v(kick) greater than or similar to 800 km s(-1), source turn-on ages t(on) greater than or similar to 20 Myr, and BATSE sampling distances 130 kpc less than or similar to d(max) less than or similar to 350 kpc. If the bursts are instead beamed with an opening half-angle theta(b), no turn-on age is required, and the model can reproduce the BATSE data for 15 degrees less than or similar to theta(b) less than or similar to 20 degrees and 80 kpc less than or similar to d(max) less than or similar to 250 kpc.
