The Xi(-)(b)pi(+)pi(-) invariant mass spectrum is investigated with an event sample of proton-proton collisions at root 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 Xi(-)(b) is reconstructed via its decays to J/psi Xi(-) and J/psi Lambda K-. A narrow resonance, labeled Xi(b)(6100)(-), is observed at a Xi(-)(b)pi(+)pi(-) invariant mass of 6100.3 +/- 0.2(stat) +/- 0.1(syst) +/- 0.6(Xi(-)(b)) MeV, where the last uncertainty reflects the precision of the Xi(-)(b) baryon mass. The upper limit on the Xi(b)(6100)(-) natural width is determined to be 1.9 MeV at 95% confidence level. The low Xi(b)(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 Xi(c) baryon states, the new Xi(b)(6100)(-) resonance and its decay sequence are consistent with the orbitally excited Xi(- )(b)baryon, with spin and parity quantum numbers J(P) = 3/2(-).