The first observation of the Σ+→pμ+μ− decay is reported with high significance using proton-proton collision data, corresponding to an integrated luminosity of 5.4fb−1, collected with the LHCb detector at a centre-of-mass energy of 13~TeV. A yield of 237±16Σ+→pμ+μ− decays is obtained, where the uncertainty is statistical only. A branching fraction of (1.08±0.17)×10−8 is measured, where the uncertainty includes statistical and systematic sources. No evidence of resonant structures is found in the dimuon invariant-mass distribution. All results are compatible with Standard Model expectations. This represents the rarest decay of a baryon ever observed.The first observation of the Σ+→pμ+μ- decay is reported with high significance using proton-proton collision data, corresponding to an integrated luminosity of 5.4 fb-1, collected with the LHCb detector at a center-of-mass energy of 13 TeV. A yield of 237±16 Σ+→pμ+μ- decays is obtained, where the uncertainty is statistical only. A branching fraction of (1.08±0.17)×10-8 is measured, where the uncertainty includes statistical and systematic sources. No evidence of resonant structures is found in the dimuon invariant-mass distribution. All results are compatible with standard model expectations. This represents the rarest decay of a baryon ever observed.The first observation of the Σ+→pμ+μ− decay is reported with high significance using proton-proton collision data, corresponding to an integrated luminosity of 5.4fb−1, collected with the LHCb detector at a centre-of-mass energy of 13~TeV. A yield of 237±16Σ+→pμ+μ− decays is obtained, where the uncertainty is statistical only. A branching fraction of (1.08±0.17)×10−8 is measured, where the uncertainty includes statistical and systematic sources. No evidence of resonant structures is found in the dimuon invariant-mass distribution. All results are compatible with Standard Model expectations. This represents the rarest decay of a baryon ever observed