  We use the chiral quark model to estimate the coefficients of the weak chiral
lagrangian as obtained from the bosonization of the ten relevant operators of
the $\Delta S = 1$ effective quark lagrangian. All contributions of order
$N_c^2$ as well as $N_c$ and $\alpha_s N_c$ are included. The chiral
coefficients are given in terms of $f_{\pi}$, the quark and gluon condensates
and the scale-dependent NLO Wilson coefficients of the corresponding operators.
In addition, they depend on the constituent quark mass $M$, a parameter
characteristic of the model. The $\gamma_5$-scheme dependence of the chiral
coefficients, computed via dimensional regularization, and the Fierz
transformation properties of the operator basis are discussed in detail. We
apply our result to the evaluation of the hadronic matrix elements for the
decay $K^0 \rightarrow 2 \pi$, consistently including the renormalization
induced by the meson loops. The effect of this renormalization is sizable and
introduces a long-distance scale dependence that matches in the physical
amplitudes the short-distance scale dependence of the Wilson coefficients.
