Using pp collision data corresponding to 1.0 fb(-1) integrated luminosity collected by the LHCb detector, two narrow states are observed in the Lambda(0)(b) pi(+) pi(-) spectrum with masses 5911.97 +/- 0.12(stat) +/- 0.02(syst) +/- 0.66(Lambda(0)(b) mass) MeV/c(2) and 5919.77 +/- 0.08(stat) +/- 0.02(syst) +/- 0.66(Lambda(0)(b) 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 Lambda(0)(b) baryons, Lambda(b)(0)(5912) and Lambda(b)(0)(5920).