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We model the annihilation of relic positrons produced in a gamma-ray burst(GRB) after its afterglow has faded. We find that the annihilation signal fromat least one GRB remnant in the Milky Way galaxy should be observable withfuture space missions such as INTEGRAL and EXIST, provided that the gassurrounding the GRB source has the typical density of the interstellar medium,< 1 cm^-3. Three fortunate circumstances conspire to make the signalobservable. First, unlike positrons in a standard supernova, the GRB positronsinitially travel at a relativistic speed and remain ahead of anynon-relativistic ejecta until the ejecta become rarefied and the annihilationtime becomes long. Second, the GRB remnant remains sufficiently hot (T > 5 x10^5 K) for a strong annihilation line to form without significant smearing bythree-photon decay of positronium. Third, the annihilation signal persists overa time longer than the average period between GRB events in the Milky Waygalaxy.Comment: 5 pages, 2 figures, submitted to ApJL (fixed Latex figure  referencing

Identifying Gamma-Ray Burst Remnants through Positron Annihilation Radiation