The parameter epsilon(K) describes CP violation in the neutral kaon system and is one of the most sensitive probes of new physics. The large uncertainties related to the charm-quark contribution to epsilon(K) have so far prevented a reliable standard-model prediction. We show that Cabibbo-Kobayashi-Maskawa unitarity enforces a unique form of the vertical bar Delta S = 2 vertical bar weak effective Lagrangian in which the short-distance theory uncertainty of the imaginary part is dramatically reduced. The uncertainty related to the charm-quark contribution is now at the percent level. We present the updated standard-model prediction epsilon(K)=2.16(6)(8)(15) x 10(-3), where the errors in parentheses correspond to QCD short-distance, long-distance, and parametric uncertainties, respectively.