This study will examine whether high-dose intravenous immunoglobulin (IVIG) is safe and effective for treating cerebellar ataxia-degeneration of the cerebellum, the part of the brain responsible for coordinating muscle movements and balance. The disease causes a slowly progressive impairment of speech and balance, with patients often developing slurred speech, tremor, clumsiness of the hands, and walking difficulties (ataxia). IVIG is derived from donated blood that has been purified, cleaned and processed into a form that can be infused. IVIG is an immune suppressant that is routinely used to treat other neurological conditions.