We present a measurement of the B0s lifetime in fully and partially reconstructed B0s→D−s(ϕπ−)X decays in 1.3  fb−1 collected in pp collisions at s√=1.96  TeV by the CDF II detector at the Fermilab Tevatron. We measure τ(B0s)=1.518±0.041(stat)±0.027(syst)  ps. The ratio of this result and the world average B0 lifetime yields τ(B0s)/τ(B0)=0.99±0.03, which is in agreement with recent theoretical predictions.