Cognitive symptoms are not currently well-managed in Veterans with schizophrenia, leading to substantially diminished quality of life. Improved treatment strategies clearly are needed. Recent studies suggest taht an overactive hippocampus is associated with cognitive deficits in the illness. Based on findings that the anti-epileptic drug levetiracetam (LEV) reduces hippocampal activity and improves cognition in other clinical populations while being safe and well-tolerated, this study will examine the effects of the drug on hippocampal activity and cognition in Veterans with schizophrenia. In this crossover design, participants will take LEV for 4 weeks and placebo pills for 4 weeks, but will not know the order in which they are taking them.