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