We perform a next-to-next-to-leading order (NNLO) QCD analysis of the
charm-top-quark contribution eta_ct to the effective Delta S = 2
Hamiltonian in the Standard Model. eta_ct represents an important part
of the short distance contribution to the parameter epsilon_K. We
calculate the three-loop anomalous dimension of the leading operator
Q_S2, the three-loop mixing of the current-current and penguin
operators into Q_S2, and the corresponding two-loop matching
conditions at the electroweak, the bottom-quark, and the charm-quark
scale. As our final numerical result we obtain eta_ct = 0.494 +/-
0.046, which is roughly 7% larger than the next-to-leading-order (NLO)
value eta_ct(NLO) = 0.455 +/- 0.069. This results in a prediction for
epsilon_K = (1.99 +/- 0.25) x 10^(-3), which corresponds to an
enhancement of approximately 3.3% with respect to the value obtained
using eta_ct(NLO).