HIV-infected twins will be admitted to the NIH Clinical Center for the first cell infusion. The gene-marked cells will be infused over a 60-minute period through a plastic tube (catheter) placed in an arm vein, or, if a suitable arm vein cannot be found, through a special catheter placed into a large vein in the neck or chest. Vital signs (temperature, pulse, blood pressure and breathing rate), blood oxygen concentration, and urine output will be monitored regularly for 24 hours. Blood samples will be collected before and after the infusion to monitor for gene-marked cells. Patients will be discharged the next day. They will return to NIH daily the first week (from Monday through Thursday) to monitor for CD4 cell counts, plasma viral burden, p24 antigen levels, HIV levels and the presence of the NeoR gene, and then weekly for the next 5 weeks for these tests and others to monitor blood and urine chemistry, blood counts and immune function markers.