  We study the parity-violating pion-nucleon coupling $G_\pi$ in the framework
of a realistic three flavor Skryme model. We find a sizeable enhancement of
$G_\pi \simeq 0.8 ... 1.3 \cdot 10^{-7}$ compared to previous calculations in
two-flavor models with vector mesons. This strangeness enhancement stems from
induced kaon fields of the chiral soliton and the non-monotoneous dependence on
symmetry breaking of the nucleon matrix element of the flavor singlet piece of
the operator associated with these induced fields. Both features are sensitive
to four quark operators including an $\bar s s$ pair.
