The time-dependent C P asymmetry in B 0 s → J / ψ K + K − decays is measured using p p collision data, corresponding to an integrated luminosity of 3.0     fb − 1 , collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. In a sample of 96 000 B 0 s → J / ψ K + K − decays, the C P -violating phase ϕ s is measured, as well as the decay widths Γ L and Γ H of the light and heavy mass eigenstates of the B 0 s - ¯ B 0 s system. The values obtained are ϕ s = − 0.058 ± 0.049 ± 0.006     rad , Γ s ≡ ( Γ L + Γ H ) / 2 = 0.6603 ± 0.0027 ± 0.0015     ps − 1 , and Δ Γ s ≡ Γ L − Γ H = 0.0805 ± 0.0091 ± 0.0032     ps − 1 , where the first uncertainty is statistical and the second, systematic. These are the most precise single measurements of those quantities to date. A combined analysis with B 0 s → J / ψ π + π − decays gives ϕ s = − 0.010 ± 0.039     rad . All measurements are in agreement with the standard model predictions. For the first time, the phase ϕ s is measured independently for each polarization state of the K + K − system and shows no evidence for polarization dependence.