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During their violent merger, two neutron stars can shed a few percent of their mass. As this ejecta expands, it collides with the surrounding interstellar gas, producing a slowly-fading radio flare that lasts for years. Radio flares uniquely probe the neutron star merger populations as many events from past decades could still be detectable. Nonetheless, no radio flare observation has been reported to date. Here we show that the radio transient FIRST J1419+3940, first observed in 1993 and still detectable, could have originated from a neutron star merger. We carry out numerical simulations of neutron star merger ejecta to demonstrate that the observed radio light curve is well reproduced by a merger model with astrophysically expected parameters. We examine the observed radio data, as well as the host galaxy, to find clues that could differentiate the transient's neutron star merger origin from the alternative explanation---the afterglow of an off-axis long gamma-ray burst. Near-future observations could find further evidence for the FIRST J1419+3940 radio transient's origin. We show that existing radio surveys likely already recorded multiple radio flares, informing us of the origin and properties of neutrons tar mergers and their role in the nucleosynthesis of the heaviest elements in the Universe.