The time-dependent CP asymmetry in B0s→J/ψK+K− decays is measured using pp collision data at √s=7  TeV, corresponding to an integrated luminosity of 1.0  fb−1, collected with the LHCb detector. The decay-time distribution is characterized by the decay widths ΓL and ΓH of the light and heavy mass eigenstates of the B0s−¯¯¯B0s system and by a CP-violating phase ϕs. In a sample of 27 617 B0s→J/ψK+K− decays, where the dominant contribution comes from B0s→J/ψϕ decays, these parameters are measured to be ϕs=0.07±0.09(stat)±0.01(syst)  rad, Γs≡(ΓL+ΓH)/2=0.663±0.005(stat)±0.006(syst)  ps−1, and ΔΓs≡ΓL−ΓH=0.100±0.016(stat)±0.003(syst)  ps−1, corresponding to the single most precise determination of ϕs, ΔΓs, and Γs. The result of performing a combined analysis with B0s→J/ψπ+π− decays gives ϕs=0.01±0.07(stat)±0.01(syst)  rad, Γs=0.661±0.004(stat)±0.006(syst)  ps−1, and ΔΓs=0.106±0.011(stat)±0.007(syst)  ps−1. All measurements are in agreement with the Standard Model predictions.