We consider a model for gamma-ray bursts (GRBs) from high-velocity neutron stars in the Galactic halo. In this model, bursters are born in the Galactic disk with large recoil velocities V_r, and GRBs are beamed to within emission cones of half-angle _b centered on V_r. We describe scenarios for magnetically channeled GRBs that have such beaming characteristics. We then make detailed comparisons of this halo beaming model (HBM) to data from the Third BATSE Catalog and from the Pioneer Venus Orbiter experiment, for both GRB intensity and angular position distributions. Acceptable fits to observations of over 1000 bursts are obtained for _b = 15°-30° and for a BATSE sampling depth of D ~ 180 kpc, which corresponds to a peak burst luminosity of ~10⁴⁰ ergs s^-1. Present data favor a truly isotropic (cosmological) model over the HBM but not by a statistically compelling margin (2 σ).

The HBM makes the distinctive prediction that the galactocentric quadrupole moment cos² Θ - for bright, nearby GRBs is large, even though the dipole moment cos Θ remains near zero. Bursters born in nearby external galaxies, such as M31, are almost entirely undetectable in the HBM because of misdirected beaming. We analyze several refinements of the basic HBM: gamma-ray intensities that vary with angle from the beam axis; non-standard candle GRB luminosity functions; and models including a subset of bursters that do not escape from the Galaxy. We also discuss the energy budgets for the bursters, the origins of their recoils, and the physics of burst beaming and alignment. One possible physical model is based on the magnetar model of soft gamma repeaters (SGRs). Empirical bounds on the rate of formation and peculiar velocities of SGRs imply that there exist ~10⁴ to ~10⁷ aged SGRs in the Galactic halo within a distance ~100 kpc.

The HBM gives an acceptable fit to observations only if it satisfies some special conditions (_b ≈ 20°; uniform bursting rate) that are possible, but for which there are no clear and compelling theoretical justifications. The cosmological burst hypothesis is more generic and thus more attractive in this sense.