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From an analysis of the decay Bs0 → J/ψφ, we obtain the width difference between the light and heavy mass eigenstates ΔΓ≡(ΓL - ΓH ) = 0.17 ± 0.09(stat) ± 0.02(syst) ps-1 and the CP-violating phase φs= -0.79 ± 0.56(stat) -0.01+0.14 (syst). Under the hypothesis of no CP violation (φs ≡ 0), we obtain 1/ Γ̅= τ̅Bs0 = 1.52 ± 0.08(stat) 0.03+0.01(syst) ps and ΔΓ 0.12-0.10+0.08(stat) ± 0.02(syst) ps-1. The data sample corresponds to an integrated luminosity of about 1.1 fb-1 accumulated with the D0 detector at the Fermilab Tevatron collider. This is the first direct measurement of the CP-violating mixing phase in the Bs0 system.