  We present a quenched lattice study of the form factors $f_+(q^2)$ and
$f_0(q^2)$ of the matrix elements $<\pi | \bar{s} \gamma_\mu u | K >$. We focus
on the second-order SU(3)-breaking quantity $[1 - f_+(0)]$, which is necessary
to extract $|V_{us}|$ from $K_{\ell 3}$ decays. For this quantity we show that
it is possible to reach the percent precision which is the required one for a
significant determination of $|V_{us}|$. The leading quenched chiral logarithms
are corrected for by using analytic calculations in quenched chiral
perturbation theory. Our final result, $f_+^{K^0\pi^-}(0) = 0.960 \pm
0.005_{\rm stat} \pm 0.007_{\rm syst}$, where the systematic error does not
include the residual quenched effects, is in good agreement with the estimate
made by Leutwyler and Roos. A comparison with other non-lattice computations
and the impact of our result on the extraction of $|V_{us}|$ are also
presented.
