Abstract: Using a data sample of pp collisions corresponding to an integrated luminosity of 3 fb(-1), the Xi(-)(b) and Omega(-)(b) baryons are reconstructed in the Xi(-)(b) -> J/psi Xi(-) and Omega(-)(b) -> J/psi Omega(-) decay modes and their lifetimes measured to be tau(Xi(-)(b)) = 1.55(-0.09)(+0.10) (stat) +/- 0.03 (syst) ps, tau(Omega(-)(b)) = 1.54(-0.21)(+0.26) (stat) +/- 0.05 (syst) ps. These are the most precise determinations to date. Both measurements are in good agreement with previous experimental results and with theoretical predictions.