The Ξb−π+π− invariant mass spectrum is investigated with an event sample of proton-proton collisions at √s=13  TeV, collected by the CMS experiment at the LHC in 2016–2018 and corresponding to an integrated luminosity of 140 fb−1. The ground state Ξb− is reconstructed via its decays to J/ψΞ− and J/ψΛK−. A narrow resonance, labeled Ξb(6100)−, is observed at a Ξb−π+π− invariant mass of 6100.3±0.2(stat)±0.1(syst)±0.6(Ξb−) MeV, where the last uncertainty reflects the precision of the Ξb− baryon mass. The upper limit on the Ξb(6100)− natural width is determined to be 1.9  MeV at 95% confidence level. The low Ξb(6100)− signal yield observed in data does not allow a measurement of the quantum numbers of the new state. However, following analogies with the established excited Ξc baryon states, the new Ξb(6100)− resonance and its decay sequence are consistent with the orbitally excited Ξb− baryon, with spin and parity quantum numbers JP=3/2−.