The observation of a new b baryon via its strong decay into Xi(-)(b)pi(+) (plus charge conjugates) is reported. The measurement uses a data sample of pp collisions at root s = 7 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 5.3 fb(-1). The known Xi(-)(b) baryon is reconstructed via the decay chain Xi(-)(b) -> J/psi Xi(-) -> mu(+)mu(-)Lambda(0)pi(-), with Lambda(0) -> p pi(-). A peak is observed in the distribution of the difference between the mass of the Xi(-)(b)pi(+) system and the sum of the masses of the Xi(-)(b) and pi(+), with a significance exceeding 5 standard deviations. The mass difference of the peak is 14.84 +/- 0.74(stat) +/- 0.28(syst) MeV. The new state most likely corresponds to the J(P) = 3/2(+) companion of the Xi(b).