  If gamma-ray bursts originate at cosmological distances then their angular
distribution should exhibit a dipole in the direction of the solar motion
relative to the cosmic microwave background. This is due to the combined
effects of abberation, an anisotropic shift of the burst event rate, and an
angular variation in the distance out to which bursts can be detected.
  We derive the amplitude of the expected dipole for an open and flat
cosmological model, and for various possible evolution rates of the burst
population. Although our dimensionless velocity with respect to the CMB rest
frame is of order $10^{-3}$, the dipole amplitude is of order $10^{-2}$, an
order of magnitude larger. The results depend very weakly on the value of
$\Omega_0$, but are sensitive to the spectral index of the bursts' photon
spectra, and to the rate of evolution of the burst population. There is no
dependence on the value of the Hubble constant.
  A clear detection of the dipole will require a larger sample of bursts than
currently available (of order $10^4$). Future statistical analyses of the
hypothesis that bursts originate at cosmological distances should take this
effect into account, rather than assuming a perfectly isotropic distribution,
for obtaining the correct statistical significance of their results.
