This is a Phase I study. This research study is being conducted to find new ways to treat severe hemophilia A. This study is a gene therapy study. Gene therapy is an experimental way to introduce, into a person's cells, specific genetic material. A gene can be delivered/introduced into a cell using a carrier known as a "vector." In this study, a virus (lentivirus), the "vector", is used to introduce or deliver a gene that creates and stores a protein Factor VIII (FVIII) in your platelets. These platelets are made from stem cells (mother cells for your bone marrow) that are removed from your blood by a procedure called apheresis. This research study will take some of the patient's own stem cells, from the apheresis procedure, and genetically modify them using the vector in order to make them produce FVIII in platelets that arise from the stem cells. They will then give the genetically modified stem cells back to the patient so that they can possibly create platelets that produce and store Factor VIII on their own.