A double-blinded, randomized, placebo-controlled study will be performed. Forty-eight individuals with a diagnosis of mild Alzheimer's disease between 60-85 years old will complete the study. There will be two cohorts of 60-75 and 75-85 years old that will be age-matched. All forty-eight individuals will have been on donepezil, which is FDA approved for the treatment of Alzheimer's disease, at a dose of 5mg or 10mg per day for at least 3 months prior to consenting and will remain on the drug throughout this study. Twenty-four mild Alzheimer's disease patients will receive riluzole and another 24 will receive a placebo (the placebo tablets will be generated at the Rockefeller University's pharmacy by the research pharmacist). All patients will have a neurological evaluation and neuropsychological tests performed to confirm that they meet criteria for probable Alzheimer's disease set out by the National Institute on Aging - Alzheimer's disease Association that recently revisited the NINCDS-ADRDA criteria and to have mild Alzheimer's disease.