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).Received 22 September 2004DOI:https://doi.org/10.1103/PhysRevLett.94.042001©2005 American Physical Society