The life-long impairments in communication and social function for those with autism are often complicated by the presence of medical comorbidities, including epilepsy, gastrointestinal disturbances, and sleep disorders. Little is known about the pathophysiology of these comorbid conditions and even less about treatment of the symptoms among individuals with autism. Sleep disorders in ASD are of particular interest and can be reliably investigated using polysomnography (PSG), a non-invasive recording of a variety of sleep parameters. A previous study showed that children with autism spend an abnormally short time in the Rapid Eye Movement (REM) stage of sleep, which is thought to play a key role in learning and memory, compared to total sleep time. Donepezil hydrochloride is a drug that has been shown to normalize REM sleep, and treatment with donepezil could benefit the quality of sleep in children with autism as well as enhance their ability to learn and remember. This pilot study aims to determine the dose of donepezil that reliably increases the percentage of REM sleep and to assess any potential side effects in children ages 2-11. If donepezil is effective in normalizing REM sleep, and the drug's side-effects profile is favorable, then a placebo-controlled trial will be initiated to assess the effects of long-term donepezil administration on REM sleep and on autistic symptoms, learning, memory, and overall behavior.