Abstract: First evidence of a structure in the J/psi Lambda invariant mass distribution is obtained from an amplitude analysis of Xi(-)(b) -> J/psi Lambda K- decays. The observed structure is consistent with being due to a charmonium pentaquark with strangeness with a significance of 3.1r including systematic uncertainties and lookelsewhere effect. Its mass and width are determined to be 4458.8 +/- 2.9(-1.1)(+4.7) MeV and 17.3 +/- 6.5(-5.7)(+8.0) MeV, respectively, where the quoted uncertainties are statistical and systematic. The structure is also consistent with being due to two resonances. In addition, the narrow excited Xi(-) states, Xi(-)(1690) and Xi(-)(1820)(-), are seen for the first time in a Xi(-)(b) decay, and their masses and widths are measured with improved precision. The analysis is performed using pp collision data corresponding to a total integrated luminosity of 9 fb(-1), collected with the LHCb experiment at centre-of-mass energies of 7, 8 and 13 TeV.