The observation of a new b baryon via its strong decay into Ξ(b)(-) π(+) (plus charge conjugates) is reported. The measurement uses a data sample of pp collisions at sqrt[s] = 7 TeV collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 5.3 fb(-1). The known Ξ(b)(-) baryon is reconstructed via the decay chain Ξ(b)(-) → J/ψΞ(-) → μ(+) μ(-) Λ(0) π(-), with Λ(0) → pπ(-). A peak is observed in the distribution of the difference between the mass of the Ξ(b)(-) π(+) system and the sum of the masses of the Ξ(b)(-) and π(+), 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 Ξ(b).