  An amplitude analysis of $B^-\to J/\psi\Lambda\bar{p}$ decays is performed
using about 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 $J/\psi\Lambda$ 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 $4338.2\pm 0.7\pm 0.4$MeV and
${7.0\pm1.2\pm1.3}$MeV, where the first uncertainty is statistical and the
second systematic. The spin is determined to be $1/2$ and negative parity is
preferred. Due to the small $Q$-value of the reaction, the most precise single
measurement of the $B^-$ mass to date, $5279.44\pm0.05\pm0.07$MeV, is obtained.
