A narrow pentaquark state, P_{c}(4312)^{+}, decaying to J/ψp, is discovered with a statistical significance of 7.3σ in a data sample of Λ_{b}^{0}→J/ψpK^{-} decays, which is an order of magnitude larger than that previously analyzed by the LHCb Collaboration. The P_{c}(4450)^{+} pentaquark structure formerly reported by LHCb is confirmed and observed to consist of two narrow overlapping peaks, P_{c}(4440)^{+} and P_{c}(4457)^{+}, where the statistical significance of this two-peak interpretation is 5.4σ. The proximity of the Σ_{c}^{+}D[over ¯]^{0} and Σ_{c}^{+}D[over ¯]^{*0} thresholds to the observed narrow peaks suggests that they play an important role in the dynamics of these states.