  We examine the effect of isospin-violating meson-nucleon coupling constants
on low-energy pion-nucleon scattering. We compute the couplings in the context
of a nonrelativistic quark model. The difference between the up and down
constituent masses induces a coupling of the neutral pion to the proton that is
slightly larger than the corresponding one for the neutron. This difference
generates a large isospin-violating correction---proportional to the
isospin-even contribution arising from the nucleon Born terms---to the
charge-exchange ($\pi^{-}p \rightarrow \pi^{0}n$) amplitude. In contrast to the
isospin-conserving case, this correction is not cancelled by $\sigma$-meson
exchange; in our model there is no isospin-violating $NN\sigma$ coupling at
$q^2=0$. As a result, we find a violation of the triangle identity consistent
with the one reported by Gibbs, Ai, and Kaufmann from a recent analysis of
pion-nucleon data.
