Abstract: A search for the rare decay Sigma(+) -> p mu(+)mu(-) is performed using pp collision data recorded by the LHCb experiment at center-of-mass energies root 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 Sigma(+) -> p mu(+)mu(-) branching fraction is (2.2(-1.3)(+1.8)) x 10(-8), where statistical and systematic uncertainties are included, which is consistent with the standard model prediction.