  Using the exclusive decay B^0_s -> J/psi (mu+mu-) phi(K+K-), we report the
most precise single measurement of the B^0_s lifetime. The data sample
corresponds to an integrated luminosity of approximately 220 pb-1 collected
with the DO detector at the Fermilab Tevatron Collider in 2002-2004. We
reconstruct 337 signal candidates, from which we extract the B^0_s lifetime,
\tau(B^0_s) = 1.444 +0.098/-0.090 stat +/- 0.020 sys ps. We also report a
measurement for the lifetime of the B^0 meson using the exclusive decay B^0 ->
J/psi (mu+mu-)K*0(892)(K+pi-). We reconstruct 1370 signal candidates, obtaining
\tau(B^0) = 1.473 +0.052/-0.050 stat +/- 0.023 sys ps, and the ratio of
lifetimes, \tau(B^0_s)/\tau(B^0) = 0.980 +0.076/-0.071 stat +/- 0.003 sys.
