This study involves patients 12 years and older who have been diagnosed with herpes simplex encephalitis (HSE) by a specific laboratory test and have completed treatment or are being treated with intravenous (given through a needle inserted into a vein) acyclovir. The purpose of the study is to determine if treatment with 4 tablets, 500 milligrams each, of valacyclovir given 3 times daily by mouth for 90 days is both effective and safe after completing intravenous acyclovir treatment and if it can increase survival with or without mild impairment of the brain and mental functions. Participants will be assigned to either drug or placebo (inactive substance) randomly (by chance). Study procedures will include blood samples and lumbar punctures (procedure in which a needle is inserted into the lower back to collect cerebral spinal fluid). Subjects will participate for up to 24 months.