Clusters of galaxies are enriched with positrons from jets of active galactic nuclei (AGNs) or from the interaction of cosmic rays with the intracluster gas. We follow the cooling of these positrons and show that their eventual annihilation with cluster electrons yields a narrow annihilation line. Unlike annihilation in the interstellar medium of galaxies, the line produced in clusters is not smeared by three-photon decay of positronium because positronium formation is suppressed at the high (approx> 1 keV) temperature of the cluster electrons. We show that if AGN jets are composed of e~+e~- pairs, then the annihilation line from rich clusters within a distance of 100 Mpc might be detectable with future space missions, such as the International Gamma-Ray Astrophysical Laboratory or the Energetic X-Ray Imaging Survey Telescope.
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