Abstract: The observation of the decay Xi(-)(b)-> J/psi Lambda K- is reported, using a data sample corresponding to an integrated luminosity of 3 fb(-1), collected by the LHCb detector in pp collisions at centre-of-mass energies of 7 and 8 TeV. The production rate of Xi(-)(b) baryons detected in the decay Xi(-)(b) -> J/psi Lambda K- is measured relative to that of Lambda(0)(b) baryons using the decay Lambda(0)(b) -> J/psi Lambda. Integrated over the b-baryon transverse momentum p(T) < 25 GeV/c and rapidity 2.0 < y < 4.5, the measured ratio is f Xi(-)(b/) f Lambda(0)(b) B(Xi(-)(b)-> J/psi Lambda K-) / B(Lambda(0)(b)-> J/psi Lambda) = (4.19 +/- 0.29 (stat) +/- 0.15 (syst)) x 10(-2), where f(Xi)(b)(-) band f(Lambda)(b)(0)are the fragmentation fractions of b ->Xi(-)(b)and b ->Lambda(0)(b)transitions, and ss represents the branching fraction of the corresponding b- baryon decay. The mass difference between Xi(-)(b) and Lambda(0)(b) baryons is measured to be M(Xi(-)(b))-M(Lambda(0)(b)) = 177.08 +/- 0.47 (stat) +/- 0.16 (syst) MeV/c(2).