A search for charge-parity (CP) violation in D-0 -> K-K+ and D-0 -> pi(-)pi(+) decays is reported, using pp collision data corresponding to an integrated luminosity of 5.9 fb(-1) collected at a center-of-mass energy of 13 TeV with the LHCb detector. The flavor of the charm meson is inferred from the charge of the pion in D* (2010)(+) -> D-0 pi(+) decays or from the charge of the muon in (B) over bar -> D-0 mu(-)(nu) over bar X-mu decays. The difference between the CP asymmetries in D-0 -> K-K+ and D-0 -> pi(-)pi(+) decays is measured to be Delta A(CP) = [-18.2 +/- 3.2(stat) +/- 0.9(syst)] x 10(-4) for pi-tagged and Delta A(CP) = [-9 +/- 8(stat) +/- 5(syst)] x 10(-4) for mu-tagged D-0 mesons. Combining these with previous LHCb results leads to Delta A(CP) = (-15.4 +/- 2.9) x 10(-4), where the uncertainty includes both statistical and systematic contributions. The measured value differs from zero by more than 5 standard deviations. This is the first observation of CP violation in the decay of charm hadrons.