The lifetime of the B^0_s meson is measured using the semileptonic
B^0_s -> D^-_s 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 decay modes are reconstructed resulting in approximately
600 D^-_s 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.