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-.