  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 = 0.496 +/- 0.047, which
is roughly 7% larger than the next-to-leading-order (NLO) value eta_ct(NLO) =
0.457 +/- 0.073. This results in a prediction for epsilon_K = (1.90 +/- 0.26) x
10^(-3), which corresponds to an enhancement of approximately 3.3% with respect
to the value obtained using eta_ct(NLO).
