This is a pilot study of hydroxyurea versus placebo to reduce central nervous system complications (abnormally fast blood flow to the brain, silent cerebral infarct or stroke) in young children with sickle cell disease. The investigators plan to identify children 12 to 48 months old without central nervous system complications and randomly assign 20 to treatment with hydroxyurea and 20 to treatment with placebo for 36 months. Neither the study doctors nor the participants will know which treatment they are receiving.