A narrow pentaquark state, \(P_c(4312)^+\), decaying to \(J/\psi p\) is discovered with a statistical significance of \(7.3\sigma\) in a data sample of \({\Lambda_b^0\to J/\psi p K^-}\) 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 \(5.4\sigma\). Proximity of the \(\Sigma_c^+\bar{D}^{0}\) and \(\Sigma_c^+\bar{D}^{*0}\) thresholds to the observed narrow peaks suggests that they play an important role in the dynamics of these states.