The lifetime of the B^0_s meson is measured using the semileptonic
decay B^0_s -> D^-_s l^+ nu X.  The data sample consists of approximately
110 pb^-1 of ppbar collisions at sqrt s = 1.8 TeV collected by the CDF
detector at the Fermilab Tevatron collider.  There are 254 +/- 21 D^-_s l^+
signal events where the D^-_s is reconstructed through its decay mode D^-_s ->
phi pi^-, phi -> K^+K^-.  Using these events, the B^0_s meson lifetime is
determined to be tau(B^0_s) = 1.37 ^+0.14 _-0.12(stat.) +/- 0.04 (syst.) ps.
The B^0_s meson proper decay length distribution has been examined for a
lifetime difference between the two CP eigenstates of the B^0_s meson, B^H_s
and B^L_s.