  Collisions of deformed uranium nuclei provide a unique opportunity to study
the spatial dependence of charmonium in-medium effects. By selecting the
orientations of the colliding nuclei, different path lengths through the
nuclear medium could be selected within the same experimental environment. In
addition, higher energy densities can be achieved in U+U collisions relative to
Au+Au collisions. In this paper, we investigate the prospects for charmonium
studies with U+U collisions. We discuss the effects of shadowing and nuclear
absorption on the J/\psi\ yield. We introduce a new observable which could help
distinguish between different types of J/\psi\ interactions in hot and dense
matter.
