The time-dependent CP asymmetry in B-s(0) -> J/psi K+ K- decays is measured using pp collision data at root 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 Gamma(L) and Gamma(H) of the light and heavy mass eigenstates of the B-s(0) ¿ (B) over barB(s)(0) system and by a CP-violating phase s. In a sample of 27 617 B-s(0) -> J/psi K+ K- decays, where the dominant contribution comes from B-s(0) -> J/psi K+ K- decays, these parameters are measured to be phi(s) = 0. 07 +/- 0.09(stat) +/- 0. 01(syst) rad, Gamma(s) equivalent to (Gamma(L) + Gamma(L))/2 = 0.663 +/- 0.005(stat) +/- 0.006(syst) ps(-1), and 0.006(syst) ps(-1), and Delta Gamma(s) equivalent to Gamma(L) ¿ Gamma(L) = 0.100 +/- 0.016(stat) +/- 0.003(syst) ps(-1), corresponding to the single most precise determination of phi(s), Delta Gamma(s), and Gamma(s.). The result of performing a combined analysis with B-s(0) -> J/psi pi(+) pi(-) decays gives phi(s) = 0.01 +/- 0.07(stat) +/- 0.01(syst)rad, Gamma(s) = 0.661 +/- 0.004(stat) +/- 0.006(syst) ps(-1), and Delta Gamma(s) = 0.106 +/- 0.011(stat) +/- 0.007(syst) ps(-1). All measurements are in agreement with the Standard Model predictions.