The lifetime of the B^0_S meson is measured using the semileptonic
decay B^0_s -> D_{s-bar} l^+ nu X.  The data sample consists of about 110
pb^-1 of ppbar collisions at sqrt s = 1.8 TeV collected by the CDF detector at
Fermilab.  Four different D_{s-bar} decay modes are reconstructed resulting in
approximately 600 D_{s-bar} l^+ signal events.  The B^0_S meson lifetime is
determined to be tau(B^0_S) = (1.36 +/- 0.09^+0.06_ -0.05) ps, where the first
and second uncertainties are statistical and systematic, respectively.  The
B^0_S meson decay length distribution is examined for a lifetime difference
Delta Gamma/Gamma between the two mass eigenstates of the B^0_S meson.  An
upper limit of Delta Gamma/Gamma < 0.83 is set at 95% confidence level.