  We report a measurement of the B^0_s meson lifetime from B_s^0 -> D^-_s X
decays, where D_s^- mesons are reconstructed in the D_s^- -> phi pi^- and D_s^-
-> K^{*0} K^- decay channels. From approximately 3.7 million hadronic Z^0
decays recorded by the OPAL detector at LEP a sample is selected containing 911
+/- 83 candidates, of which 519 +/- 136 are estimated to be from B_s^0 meson
decays. Fitting the distribution of the distance from the beam spot to the
decay vertex of the D_s^- candidates with an unbinned likelihood function we
measure
  tau(B_s^0) = 1.72 + 0.20 - 0.19 + 0.18 - 0.17 ps,
  where the errors are statistical and systematic, respectively.
