Despite their importance, very few RR Lyrae (RRL) stars have been known to reside in binary systems. We report on a search for binary RRL in the OGLE-III Galactic bulge data. Our approach consists in the search for evidence of the light-travel time effect in so-called observed minus calculated ($O-C$) diagrams. Analysis of 1952 well-observed fundamental-mode RRL in the OGLE-III data revealed an initial sample of 29 candidates. We used the recently released OGLE-IV data to extend the baselines up to 17 years, leading to a final sample of 12 firm binary candidates. We provide $O-C$ diagrams and binary parameters for this final sample, and also discuss the properties of 8 additional candidate binaries whose parameters cannot be firmly determined at present. We also estimate that $gtrsim 4$ per cent of the RRL reside in binary systems.
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