This study will examine the safety and effectiveness of an experimental drug called GDNF delivered through an investigational device to treat progressive supranuclear palsy (PSP). The drug will be administered directly into the brain through catheters attached to an infusion pump implanted in the abdomen. The study will evaluate 1) if the drug is safe and well tolerated when given by this method; 2) the performance of the catheters and pump system, and 3) the effects of GDNF on PSP symptoms.