  We study leptoproduction of $J/\psi$ at large $Q^2$ within the
nonrelativistic QCD (NRQCD) factorization formalism. The cross section is
dominated by color-octet terms that are of order $\alpha_s$. The color-singlet
term, which is of order $\alpha^2_s$, is shown to be a small contribution to
the total cross section. We also calculate the tree diagrams for color-octet
production at order $\alpha^2_s$ in a region of phase space where there is no
leading color-octet contribution. We find that in this regime the color-singlet
contribution dominates. We argue that non-perturbative corrections arising from
diffractive leptoproduction, higher twist effects, and higher order terms in
the NRQCD velocity expansion should be suppressed as $Q^2$ is increased.
Therefore, the color-octet matrix elements $< {\cal O}_8^{\psi}(^1S_0)>$ and
$<{\cal O}_8^{\psi}(^3P_0)>$ can be reliably extracted from this process.
Finally, we point out that an experimental measurement of the polarization of
leptoproduced $J/\psi$ will provide an excellent test of the NRQCD
factorization formalism.
