  The analyses of large transverse momentum charmonium production at the
Tevatron have shown that fragmentation of gluons is an important production
mechanism. We study large-$p_T$ charmonium production in $pp$ collisions at the
LHC, and find that due to the copious gluon production at this energy, the
gluon fragmentation contribution completely overwhelms the fusion contribution
and the charm quark fragmentation contribution. Our analysis shows that for
$J/\psi$ production at the LHC, there is a significant event rate even for $p_T
\sim$~100~GeV. The measurement of the cross-section at such large values of
$p_T$ will provide a very important test of the fragmentation mechanism.
