The lifetime of the B^0_s meson is measured using the exclusive
decay mode B^0_s -> J/psi phi, where J/psi -> mu^+mu^- and phi -> K^+K^-.  The
data sample consists of 110 pb^-1 of ppbar collisions at sqrt s = 1.8 TeV,
collected by the CDF detector at the Fermilab Tevatron collider during
1992-1995.  We find 58 +/- 12 signal events, and the B^0_s meson lifetime is
determined to be tau_B^0_s = 1.34^+0.23_-0.19 (stat) +/- 0_05 (syst) ps.  This
result is consistent with previous measurements of the B^0-s, B^+, and B^0_d
meson lifetimes and with theoretical predictions.