  A recent observation of the 511 keV electron-positron annihilation line from
the Galactic bulge has prompted a debate on the origin of the galactic
positrons responsible for this emission. Assuming equilibrium between
annihilation and injection of positrons in the Galaxy, we investigate the
possibility that positrons were produced by past gamma ray bursts (GRBs). We
compare the positron annihilation rate inferred from the observed 511 keV line
with the predicted injection rate due to electron-positron pairs leaking out of
individual GRBs and those pairs produced by GRB photons in the dense molecular
clouds at the Galactic center. We conclude that the proposed scenario is
marginally consistent with observations, and can reproduce the observed
normalization of the annihilation line only for higher-than-average values of
the GRB rate in the Galaxy and/or the molecular clouds optical depth for pair
production.
