A search for the rare decay $Sigma^+ to p mu^+ mu^-$ is performed using $pp$ collision data recorded by the LHCb experiment at centre-of-mass energies $sqrt{s} = 7$ and $8$ TeV, corresponding to an integrated luminosity of $3 fb^{-1}$. An excess of events is observed with respect to the background expectations with a signal significance of 4.0 standard deviations. No significant structure is observed in the dimuon invariant mass distribution.