  The masses of charmonium states immersed in nuclear matter are calculated in
LO QCD and in QCD sum rules. While the mass shift for $J/\psi$ are found to be
less than -10 MeV, those for the $\chi_{0,1,2}$ and $\psi(3686)$ and
$\psi(3770)$ are found to be more than -40 MeV. We investigate the feasibility
of observing such mass shifts in the future accelerator project at GSI.
