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Using the exclusive decay Bs0 → J/ψ(μ+μ-)Φ(K+K-), we report the most precise single measurement of the Bs0 lifetime. The data sample corresponds to an integrated luminosity of approximately 220 pb-1 collected with the D0 detector at the Fermilab Tevatron Collider in 2002–2004. We reconstruct 337 signal candidates, from which we extract the Bs0 lifetime, τ(Bs0) = 1.444-0.090+0.098(stat) ± 0.020(sys) ps. We also report a measurement for the lifetime of the B0 meson using the exclusive decay B0 → J/ψ(μ+μ-)K+0(892)( K+π-). We reconstruct 1370 signal candidates, obtaining τ(B0) = 1.473-0.050-0.052 (stat) ± 0.023(sys) ps, and the ratio of lifetimes, τ(Bs0)/ τ(B0) = 0.980-0.071+0.076 (stat) ± 0.003(sys).