  The time-dependent CP asymmetry in B_s^0\to J/\psi K^+K^- decays is measured
using $pp$ collision data at \sqrt{s}=7TeV, corresponding to an integrated
luminosity of 1.0fb^-1, collected with the LHCb detector. The decay time
distribution is characterised by the decay widths \Gamma_L and \Gamma_H of the
light and heavy mass eigenstates of the B_s^0--\bar{B}_s^0 system and by a
CP-violating phase \phi_s. In a sample of 27\,617 B_s^0\to J/\psi K^+K^-
decays, where the dominant contribution comes from B_s^0\to J/\psi\phi\ decays,
these parameters are measured to be
  \phi_s = 0.07 \pm 0.09 (stat) \pm 0.01 (syst) rad,
  \Gamma_s \equiv (\Gamma_L+\Gamma_H)/2 = 0.663 \pm 0.005 (stat) \pm 0.006
(syst) ps^-1,
  \Delta\Gamma_s \equiv \Gamma_L -\Gamma_H = 0.100 \pm 0.016 (stat) \pm 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} \to J/\psi \pi^+\pi^- decays gives
  \phi_s = 0.01 \pm 0.07 (stat) \pm 0.01 (syst) rad,
  \Gamma_s = 0.661 \pm 0.004 (stat) \pm 0.006 (syst) ps^-1,
  \Delta\Gamma_s = 0.106 \pm 0.011 (stat) \pm 0.007 (syst) & ps^-1.
  All measurements are in agreement with the Standard Model predictions.
