This study will determine whether a drug called idebenone is safe and effective in reducing the level of oxidants that are believed to damage the nervous system and hearts in patients with Friedreich's ataxia. Friedreich's ataxia is caused by an abnormality in the gene that makes a protein called frataxin, which is necessary for the proper functioning of energy-producing parts of cells called mitrochondria. In Friedreich's ataxia, the mitochondria become overloaded with iron, and high levels of harmful compounds called oxidants are formed. These oxidants are believed to damage the cells of the nervous system and hearts of people with Friedreich's ataxia. Idebenone is a man-made drug similar to a naturally occurring compound known as Coenzyme Q10. This study will test whether idebenone can alleviate some of the symptoms of Friedreich's ataxia and slow or halt the progression of the disease.