Measurement of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>-Violating Phase<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ϕ</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math>in the Decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>B</mml:mi><mml:mi>s</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:mo>→</mml:mo><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi><mml:mi>ϕ</mml:mi></mml:math>

We present a measurement of the time-dependent CP-violating asymmetry in B(s)(0) → J/ψϕ decays, using data collected with the LHCb detector at the LHC. The decay time distribution of B(s)(0) → J/ψϕ is characterized by the decay widths Γ(H) and Γ(L) of the heavy and light mass eigenstates, respectively, of the B(s)(0) - B(s)(0) system and by a CP-violating phase ϕ(s). In a sample of about 8500 B(s)(0) → J/ψϕ events isolated from 0.37 fb(-1) of pp collisions at sqrt[s] = 7 TeV, we measure ϕ(s) = 0.15 ± 0.18(stat) ± 0.06(syst) rad. We also find an average B(s)(0) decay width Γ(s) ≡ (Γ(L) + Γ(H))/2 = 0.657 ± 0.009(stat) ± 0.008(syst) ps(-1) and a decay width difference ΔΓ(s) ≡ Γ(L) - Γ(H) = 0.123 ± 0.029(stat) ± 0.011(syst) ps(-1). Our measurement is insensitive to the transformation (ϕ(s),ΔΓ(s)) ↦ (π - ϕ(s), -ΔΓ(s)).