Two structures are observed close to the kinematic threshold in the Ξ0bπ− mass spectrum in a sample of proton-proton collision data, corresponding to an integrated luminosity of 3.0 fb−1, recorded by the LHCb experiment. In the quark model, two baryonic resonances with quark content bds are expected in this mass region: the spin-parity JP=(1/2)+ and JP=(3/2)+ states, denoted Ξ'−b and Ξ*−b. Interpreting the structures as these resonances, we measure the mass differences and the width of the heavier state to be m(Ξ'−b)−m(Ξ0b)−m(π−)=3.653±0.018±0.006 MeV/c2, m(Ξ*−b)−m(Ξ0b)−m(π−)=23.96±0.12±0.06 MeV/c2, Γ(Ξ*−b)=1.65±0.31±0.10 MeV, where the first and second uncertainties are statistical and systematic, respectively. The width of the lighter state is consistent with zero, and we place an upper limit of Γ(Ξ'−b)<0.08 MeV at 95% confidence level. Relative production rates of these states are also reported.Received 18 November 2014DOI:https://doi.org/10.1103/PhysRevLett.114.062004This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.© 2015 CERN, for the LHCb Collaboration