  The interaction of quarkonium with nuclei is studied in the $m_Q\rightarrow
\infty$ limit of QCD, where the binding energy is found to be exactly
computable. The dominant contribution to the interaction is from two-gluon
operators. The forward matrix elements of these two-gluon operators can be
determined from the QCD scale anomaly, and from deep inelastic scattering. We
apply our results to the $\Upsilon$ and $J/\psi$, treating the $\qqbar$
interaction as purely Coulombic. We find the $\Upsilon$ binds in nuclear matter
with a binding energy of a few $\mev$, while for the $J/\psi$ binding is of
order 10 $\mev$. For the $J/\psi$ in particular we expect confinement effects
to produce large corrections to this result.
