The time-dependent CP asymmetry in Bs0→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 Bs0-B̄s0 system and by a CP-violating phase s. In a sample of 27 617 Bs0→J/ψK+K- decays, where the dominant contribution comes from Bs0→J/ψ decays, these parameters are measured to be s=0.07±0.09(stat) ±0.01(syst) rad, Γs≡(ΓL+Γ H)/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 s, ΔΓs, and Γs. The result of performing a combined analysis with Bs0→J/ψπ+π- decays gives s=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. © 2013 CERN. Published by the American Physical Society under the terms of the http://creativecommons.org/licenses/by/3.0/ Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.