Leukocyte Adhesion Deficiency (LAD) is an inherited disorder of leukocyte function. Patients are profoundly immunocompromised and plagued early in life with recurrent and often life threatening infections. Allogeneic stem cell transplantation significantly improves immune function in patients LAD however severe toxicities are associated with conventional approaches to treatment. The primary objective of this phase II study is to investigate efficacy of a novel approach to allogeneic stem cell transplantation that is designed to promote partial or complete donor stem cell engraftment (hematopoietic chimerism) with reduced transplant morbidity and mortality. In an attempt to reduce toxicity from pre-transplant bone marrow conditioning, a highly immunosuppressive, low intensity bone marrow conditioning regimen will be used. Patients will be transplanted with peripheral blood stem cells from an HLA identical family member. T-lymphocytes will be removed from the stem cell graft in an attempt to decrease the risk of graft vs host disease. Donor T-cells will be infused at various time points following the transplant to augment donor hematopoietic chimerism and aid in immune reconstitution. The primary end points of this study are the establishment of donor hematopoietic chimerism, acute and chronic graft versus host disease, and transplant related mortality.