There are no approved medications that are neuroprotective or able to slow disability accumulation in secondary progressive multiple sclerosis (SPMS). This two-year study will determine if daily oral intake of lipoic acid, a natural supplement, will prove superior to placebo in reducing injury to the brain and reducing disability progression in SPMS. Neuroprotection will be measured by the extent of brain volume loss seen on MRI, and disability will be measured by neurological status and quality of life.