We study, in the context of the Kobayashi-Maskawa model, the effects that quantum chromodynamics has on the predictions for CP violation in kaon decays. We derive an effective hamiltonian for ΔS = 1 transitions in which all-order corrections in the strong coupling constant α s are incorporated, including those arising from penguin diagrams. We examine, in particular, the predictions of this hamiltonian for the ratio of the CP-violating parameters | ϵ′/ ϵ|. Our results for this ratio are well within the present experimental bound, but are considerably smaller than the recent calculation of Gilman and Wise. The discrepancy between our results and those of Gilman and Wise arises because of the different way we have estimated the amplitude for K 0 decay. A discussion of the reliability of both our estimate and that of Gilman and Wise is included.