The purpose of this phase II study is to assess the safety and efficacy of up to two intravenous infusions of autologous volume and red blood cell reduced nucleated umbilical cord blood cells as compared with placebo in neonates with neonatal encephalopathy undergoing hypothermia treatment. Efficacy will be estimated by one year survival and score on Bayley III scores in all three domains equal to or greater than 85. This will be a randomized, double-blind, placebo controlled multi-site trial of up to 160 infants who qualify for cooling.