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.