Using pp collision data corresponding to 1.0 fb(-1) integrated luminosity collected by the LHCb detector, two narrow states are observed in the Λ(b)(0)π(+)π(-) spectrum with masses 5911.97±0.12(stat)±0.02(syst)±0.66(Λ(b)(0) mass) MeV/c(2) and 5919.77±0.08(stat)±0.02(syst)±0.66(Λ(b)(0) mass) MeV/c(2). The significances of the observations are 5.2 and 10.2 standard deviations, respectively. These states are interpreted as the orbitally excited Λ(b)(0) baryons, Λ(b)(*0)(5912) and Λ(b)(*0)(5920).