We present a study of the decay B0s→J/ψϕ. We obtain the CP-odd fraction in the final state at time zero, R⊥=0.16±0.10(stat)±0.02(syst), the average lifetime of the (B0s, ¯¯¯B0s) system, ¯τ(B0s)=1.39+0.13−0.16(stat)+0.01−0.02(syst) ps, and the relative width difference between the heavy and light mass eigenstates, ΔΓ/¯¯¯Γ≡(ΓL−ΓH)/¯¯¯Γ=0.24+0.28−0.38(stat)+0.03−0.04(syst). With the additional constraint from the world average of the B0s lifetime measurements using semileptonic decays, we find ¯τ(B0s)=1.39±0.06 ps and ΔΓ/¯¯¯Γ=0.25+0.14−0.15. For the ratio of the B0s and B0 lifetimes we obtain ¯τ(B0s)τ(B0)=0.91±0.09(stat)±0.003(syst).Received 20 July 2005DOI:https://doi.org/10.1103/PhysRevLett.95.171801©2005 American Physical Society