  The gluon-exchange contribution to $J/\psi$-nucleon scattering is shown to
yield a sizeable scattering length of about -0.25 fm, which is consistent with
the sparse available data. Hadronic corrections to gluon exchange which are
generated by $\rho\pi$ and $D\bar D$ intermediate states of the $J/\psi$ are
shown to be negligible. We also propose a new method to study $J/\psi$-nucleon
elastic scattering in the reaction $\pi^+ d\to J/\psi p p$.
