We measure the mean lifetime τ=2/(ΓL+ΓH) and the decay-width difference ΔΓ=ΓL−ΓH of the light and heavy mass eigenstates of the B0s meson, B0sL and B0sH, in B0s→J/ψϕ decays using 1.7  fb−1 of data collected with the CDF II detector at the Fermilab Tevatron pp¯ collider. Assuming CP conservation, a good approximation for the B0s system in the standard model, we obtain ΔΓ=0.076+0.059−0.063(stat)±0.006(syst)  ps−1 and τ=1.52±0.04(stat)±0.02(syst)  ps, the most precise measurements to date. Our constraints on the weak phase and ΔΓ are consistent with CP conservation.