The patient will also have regular blood tests done to follow counts and the viral infection. To learn more about the way the T cells are working in the patient's body, up to an extra 30-40 ml (6-8 teaspoons) of blood will be taken before the infusion and then at 1, 2, 4, 6, and 8 weeks and 3 months. Blood should come from the central intravenous line, and should not require extra needle sticks. Total time participation for this study will be 1 year.