  We consider the predictions of chiral perturbation theory for $SU(3)$
breaking in weak semileptonic and $s$-wave nonleptonic hyperon decays. By
defining an expansion sensitive only to $SU(3)$ breaking, we show that the
leading corrections give rise to moderate corrections to $SU(3)$ relations
($\lsim 20\%$), even though the {\it chiral} symmetry $SU(3) \times SU(3)$
appears to be rather badly broken. This explains why $SU(3)$ fits to weak
hyperon decays work well even though chiral-symmetry breaking corrections are
large. Applying these $SU(3)$-breaking corrections to the analysis of the EMC
data, we find that the predicted value of $\bra p\mybar s\gamma_\mu\gamma_5
s\ket p$ is reduced by $\simeq 35\%$, suggesting that the ``EMC effect'' may be
less striking than commonly thought.
