The screening phase will last between 1 and 2 weeks. Patients will be provided with a digital blood pressure monitor with an appropriately sized cuff and be instructed to perform daily blood pressure measurements and keep a blood pressure log. This will detect severe hypertension that needs immediate attention and identify patients or families in which compliance problems likely to compromise data collection. Blood tests will be done to determine eligibility based on clinical laboratory parameters and 10ml of blood will be sent to the research laboratory for measurement of erythropoetin, ADMA, MCP-1 and possibly other modulators of vascular tone. Girls who are post-menarche will have a urine or serum pregnancy test. Prior to the initiation of any study procedures, informed consent and child assent (if appropriate) will be obtained from the participant and parents. Immediately prior to the initiation of the treatment or placebo phase 24-hour ambulatory blood pressure monitoring (ABPM #1) will be performed. Urinary nitrates and protein to creatinine ratio will be measured as surrogates for NOS activation and ongoing renal damage. At the end of the screening phase, eligible patients will be randomly assigned to either placebo or allopurinol for the active phase. Children will receive the other during the crossover phase. The purpose of this blinding is to remove either participant or investigator bias from the acquisition of the data.