This study will examine the effectiveness of an experimental treatment to improve hand function in patients who have had a stroke affecting one side of the body. One of the main problems of stroke patients is difficulty using the affected hand. Most treatments focus on acute (early) intervention, although special exercises may help some chronic patients. Previous studies have indicated that combining hand exercises with anesthesia (blocking motor and sensory function) of the upper arm may improve hand movement in stroke patients, even in the chronic state. This study will examine whether the exercise plus anesthesia treatment is more beneficial for these patients over the long-term than exercise alone.