Using pp collision data corresponding to an integrated luminosity of 1.0 fb(-1) and collected by LHCb in 2011 at a center-of-mass energy of 7 TeV, we report the measurement of direct CP violation in B-s(0) -> K-pi(+) decays, A(CP) (B-s(0) -> K-pi(+)) = 0.27 +/- 0.04(stat) +/- 0.01(syst), with significance exceeding 5 standard deviations. This is the first observation of CP violation in the decays of B-s(0) mesons. Furthermore, we provide an improved determination of direct CP violation in B-0 -> K+pi(-) decays, A(CP)(B-0 -> K+pi(-) ) = -0.080 +/- 0.007(stat) +/- 0.003(syst), which is the most precise measurement of this quantity to date.