  We calculate the cross sections for dissociation of $J/\psi$ by pions and
$\rho$-mesons within the framework of a meson exchange model. We find that
these cross sections are small at center-of-mass energies less than 1 GeV above
threshold, and that dissociation rates are less than 0.01 $c$/fm in a thermal
meson gas at temperatures where such a description makes sense.
