Using a proton-proton collision data sample collected by the LHCb experiment, corresponding to an integrated luminosity of 8.5 fb(-1), the observation of a new excited Xi(0)(b) resonance decaying to the Xi(-)(b)pi(+) final state is presented. The state, referred to as Xi(b) (6227)(0), has a measured mass and natural width of m(Xi(b)(6227)(0)) = 6227.1(-1.5)(+1.4) +/- 0.5 MeV and Gamma(Xi(b)(6227)(0)) = 18.6(-4.1)(+5.0) +/- 1.4 MeV, where the uncertainties are statistical and systematic. The production rate of the Xi(b)(6227)(0) state relative to that of the Xi(-)(b) baryon in the kinematic region 2 < eta < 5 and p(T) < 30 GeV is measured to be f(Xi b(6227)0)/f(Xi b)(-) B(Xi(b)(6227)(0) -> Xi(-)(b)pi(+)) = 0.045 +/- 0.008 +/- 0.004, where B(Xi(b)(6227)(0) -> Xi(-)(b)pi(+)) is the branching fraction of the decay, and f(Xi b(6227)0) and f(Xi b-) represent fragmentation fractions. Improved measurements of the mass and natural width of the previously observedf Xi(b)(6227)(-) state, along with the mass of the Xi(-)(b) baryon, are also reported. Both measurements are significantly more precise than, and consistent with, previously reported values.