The purpose of this 16-week research study is to determine whether a drug called memantine hydrochloride (memantine) has the potential to help improve memory and other cognitive abilities of young adults with Down syndrome (DS). Memantine (Namenda®) is a drug approved by the Food and Drug Administration (FDA) for patients with moderate to severe Alzheimer-type dementia. About 40 persons of both genders with Down syndrome aged 18-32 years will take part in this study. This is a randomized and double blind study. This means that subjects will have a 50/50 chance of being assigned to receive either the memantine pills or placebo (inactive pills). Neither the study participants nor the research personnel will know who is receiving active medication or placebo. Based on memantine's mode of action, current knowledge on brain pathology in persons with Down syndrome, and some preclinical data on mouse models of Down syndrome, we hypothesize that memantine may improve test scores of young adults with Down Syndrome on memory tests targeted at the function of the brain structure called the hippocampus. This research project has three specific aims: 1) investigate whether memantine has the potential to improve test scores on hippocampus-dependent measures in young adults with Down syndrome; 2) investigate whether memantine has the potential to improve test scores by these subjects on other cognitive measures; 3) investigate whether memantine is well tolerated by these subjects.