© 2019 CERN. for the LHCb Collaboration. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP 3 . A narrow pentaquark state, Pc(4312)+, decaying to J/ψp, is discovered with a statistical significance of 7.3σ in a data sample of Λb0→J/ψpK- decays, which is an order of magnitude larger than that previously analyzed by the LHCb Collaboration. The Pc(4450)+ pentaquark structure formerly reported by LHCb is confirmed and observed to consist of two narrow overlapping peaks, Pc(4440)+ and Pc(4457)+, where the statistical significance of this two-peak interpretation is 5.4σ. The proximity of the ςc+D̄0 and ςc+D̄∗0 thresholds to the observed narrow peaks suggests that they play an important role in the dynamics of these states.