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A search for the rare decay Σ + → p μ + μ − is performed using p p collision data recorded by the LHCb experiment at center-of-mass energies √ s = 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb − 1 . An excess of events is observed with respect to the background expectation, with a signal significance of 4.1 standard deviations. No significant structure is observed in the dimuon invariant mass distribution, in contrast with a previous result from the HyperCP experiment. The measured Σ + → p μ + μ − branching fraction is ( 2.2 + 1.8 − 1.3 ) × 10 − 8 , where statistical and systematic uncertainties are included, which is consistent with the standard model prediction.