We report the first evidence for the decay Sigma+ -> p mu+ mu- from data taken by the HyperCP experiment(E871) at Fermilab. Based on three observed events, the branching ratio is B(Sigma+ -> p,mu+,mu-) = [8.6 +6.6,-5.4(stat) +/-5.5(syst)] x 10**-8. The narrow range of dimuon masses may indicate that the decay proceeds via a neutral intermediate state, Sigma+ -> p P0, P0 -> mu+ mu-, with a P0 mass of 214.3 +/- 0.5 MeV/c**2 and branching ratio B(Sigma+ -> p P0; P0 -> mu+ mu-) = [3.1 +2.4,-1.(stat) +/-1.5(syst)] x 10**-8.