RR Lyrae pulsating stars have been extensively used as tracers of old stellar populations for the purpose of determining the ages of galaxies, and as tools to measure distances to nearby galaxies. There was accordingly considerable interest when the RR Lyr star OGLE-BLG-RRLYR-02792 was found to be a member in an eclipsing binary system4, as the mass of the pulsator (hitherto constrained only by models) could be unambiguously determined. Here we report that RRLYR-02792 has a mass of 0.26 M_sun and therefore cannot be a classical RR Lyrae star. Through models we find that its properties are best explained by the evolution of a close binary system that started with 1.4 M_sun and 0.8 M_sun stars orbiting each other with an initial period of 2.9 days. Mass exchange over 5.4 Gyr produced the observed system, which is now in a very short-lived phase where the physical properties of the pulsator happen to place it in the same instability strip of the H-R diagram occupied by RR Lyrae stars. We estimate that samples of RR Lyr stars may contain a 0.2 percent contamination with systems similar to this one, implying that distances measured with RR Lyrae stars should not be significantly affected by these binary interlopers.