We report the observation of a new structure in the Λ_{b}^{0}π^{+}π^{-} spectrum using the full LHCb data set of pp collisions, corresponding to an integrated luminosity of 9 fb^{-1}, collected at sqrt[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_{Λ_{b}(6146)^{0}}=6146.17±0.33±0.22±0.16 MeV,m_{Λ_{b}(6152)^{0}}=6152.51±0.26±0.22±0.16 MeV,Γ_{Λ_{b}(6146)^{0}}=2.9±1.3±0.3 MeV,Γ_{Λ_{b}(6152)^{0}}=2.1±0.8±0.3 MeV,with a mass splitting of Δm=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 Λ_{b}^{0} baryon. The measured masses and widths of these new excited states suggest their possible interpretation as a doublet of Λ_{b}(1D)^{0} states.