We perform a search for near-threshold I (b) (0) resonances decaying to I (b) (-) pi (+) in a sample of proton-proton collision data corresponding to an integrated luminosity of 3 fb(-1) collected by the LHCb experiment. We observe one resonant state, with the following properties: m(Xi b0) - m (Xi b-) - m (pi+) = 15.727 +/- 0.068 (stat) +/- 0.023 (syst) MeV/c2, Gamma(Xi b0) = 0.90 +/- 0.16 (stat) +/- 0.08 (syst) MeV. This confirms the previous observation by the CMS collaboration. The state is consistent with the J (P) = 3/2(+)aEuro integral I (b) (au 0) resonance expected in the quark model. This is the most precise determination of the mass and the first measurement of the natural width of this state. We have also measured the ratio sigma(pp -> Xi b0 X)B(Xi b0 -> Xi b-pi+)/sigma(pp -> Xi b- X) = 0.28 +/- 0.03 (stat.) +/- 0.01 (syst).