 The primary objective of this study is to determine the efficacy of a single intravenous infusion of unrelated donor umbilical cord blood UCB for improving functional outcomes in patients with ischemic stroke. Eligible subjects will receive an intravenous infusion of UCB or placebo 3-10 days following stroke. Subjects will not receive immunosuppressive or myeloablative medications prior to the infusion. Subjects will be followed for one year post infusion for safety and efficacy. Assessments will examine safety and tolerability of the infusion, change in neurological symptoms, change in quality of life, and emotional and cognitive status. Assessments will occur at 24 hours post infusion, and at 30, 90, 180 and 365 days post infusion. 