The lifetime of Lambda^0_b is measured using the semileptonic
decay Lambda^0_b -> Lambda^+_c l^- nu-bar, where the Lambda^+_c is
reconstructed through its decay Lambda^+_c -> pK^- pi^+.  The data were
collected by the CDF detector at the Tevatron Collider during 1992-1993 and
correspond to an integrated luminosity of 110 pb^-1 of ppbar
collisions at sqrt s = 1.8 TeV.  From a fit to the decay length distribution
of the Lambda_c- lepton system from 197 +/- 25 signal events, the lifetime of
Lambda^0_b is measured to be 1.32 +/- 0.15 +/- 0.07 ps.