The lifetime of the B_s meson is measured using the semileptonic
decay B_s -> D^-_s l^+ nu X.  The data sample consists of 19.3 pb^-1 of
ppbar collisions at sqrt s = 1.8 TeV collected by the Collider Detector at
Fermilab during 1992-1993.  There are 76 +/- 8 l^+D^-_s signal events where
the D_s is identified via the decay D^-_s -> phi pi^-, phi -> K^+K^-.  Using
these events, the B_s meson lifetime is determined to be tau_s =
142^+0.27_-0.23(stat) plus/minus 0.11 (syst) ps.  A measurment of the B_s
lifetime in a low statistics sample of exclusive B_s -> j/psi phi decays is
also presented in this paper.