The purpose of this study is to test whether long term treatment with acyclovir given orally (by mouth) improves the outcome for infants with herpes simplex virus infection of the brain or spinal cord (known as the central nervous system [CNS]). Infants with herpes viral infection of the CNS that has or has not spread to other parts of the body will be enrolled in this study. All participants will receive treatment in a hospital for 21 days with acyclovir, given intravenously (by a needle inserted into a vein). Participants will then be divided into two groups: those with CNS disease that has or has not spread to the skin, and those whose viral infection has spread and involves the CNS. Both groups will be randomly assigned to receive either oral acyclovir or placebo (inactive substance) for 6 months. Infants in the US and Canada will participate for 5 years. A physical exam, hearing exam, eye exam, and an evaluation of the nervous system will be performed throughout the study.