We report the observation of a new structure in the Lambda(0)(b)pi(+)pi(- )spectrum using the full LHCb data set of pp collisions, corresponding to an integrated luminosity of 9 fb(-1), collected at root s = 7, 8, and 13 TeV. A study of the structure suggests its interpretation as a superposition of two almost degenerate narrow states. The masses and widths of these states are measured to be m(Lambda b(6146)0) = 6146.17 +/- 0.33 +/- 0.22 +/- 0.16 MeV, m(Lambda b(6152)0) = 6152.51 +/- 0.26 +/- 0.22 +/- 0.16 MeV, Gamma(Lambda b(6146)0) = 2.9 +/- 1.3 +/- 0.3 MeV, Gamma(Lambda b(6152)0) = 2.1 +/- 0.8 +/- 0.3 MeV,with a mass splitting of Delta m = 6.34 +/- 0.32 +/- 0.02 MeV, where the first uncertainty is statistical, the second systematic. The third uncertainty for the mass measurements derives from the knowledge of the mass of the Lambda(0)(b) baryon. The measured masses and widths of these new excited states suggest their possible interpretation as a doublet of Lambda(b)(1D)(0) states.