An amplitude analysis of B^{-}→J/ψΛp[over ¯] decays is performed using 4400 signal candidates selected on a data sample of pp collisions recorded at center-of-mass energies of 7, 8, and 13 TeV with the LHCb detector, corresponding to an integrated luminosity of 9 fb^{-1}. A narrow resonance in the J/ψΛ system, consistent with a pentaquark candidate with strangeness, is observed with high significance. The mass and the width of this new state are measured to be 4338.2±0.7±0.4 MeV and 7.0±1.2±1.3 MeV, where the first uncertainty is statistical and the second systematic. The spin is determined to be 1/2 and negative parity is preferred. Because of the small Q-value of the reaction, the most precise single measurement of the B^{-} mass to date, 5279.44±0.05±0.07 MeV, is obtained.