The main goal of this study is to find out if the blood disorder called transfusion-dependent beta thalassemia can be safely treated by modifying blood stem cells. This is done by collecting blood stem cells from the subject, modifying those cells, adding a healthy beta globin gene, and then giving them back to the subject. It is hoped that these modified cells will decrease the need for blood transfusions. The gene modified blood stem cells are called CHOP-ALS20 ("study drug"). This experimental gene therapy has not been tried on human beings before and is not FDA approved.