Inclusion Criteria: * ≥2.0 months of age at initiation of busulfan conditioning * New diagnosis of typical or minimally leaky ART-SCID, as defined by the criteria below: * Artemis deficiency with bi-allelic pathogenic or likely pathogenic mutations in DCLRE1C; AND * CD3 count \< 50 autologous cells/µL (typical ART-SCID) OR spontaneous maternal chimerism, OR CD3 count \>50/µL and \<300/uL and with restricted T cell receptor Vb diversity; AND * CD45 cell response to mitogens (PHA) \< 50% of the lower limit of normal range for the lab (leaky ART-SCID). * No medically eligible HLA-identical sibling with a normal immune system who could serve as an allogeneic bone marrow donor (applies to newly diagnosed patients only). Exclusion Criteria: * Presence of a medically eligible HLA-matched sibling * Evidence of HIV infection by polymerase chain reaction or p24 antigen testing. * Unable to tolerate general anesthesia and/or marrow harvest or insertion of central venous catheter. * Any one of liver function tests AST, ALT, gamma-glutamyl transpeptidase (GGT) \>5X the upper limit of normal for lab and/or total bilirubin \>2.0 mg/dl (not due to Gilbert's) at the time of planned initiation of busulfan conditioning unless the elevated LFTs are considered to be due to medication, a viral infection for which there is no treatment other than reconstituting T cell immunity, or maternal GVHD. * Presence of any severe medical conditions making a patient unsuitable for busulfan administration * Presence of a recognized second gene mutation that results in an autosomal dominant or recessive disorder intrinsic to hematopoietic cells and that could be treated by an allogeneic HCT. * Presence of a medical condition indicating that survival is predicted to be less than 4 months, such as the requirement for mechanical ventilation, severe failure of a major organ system, or evidence of a serious, progressive infection that is refractory to medical therapy. * A social situation indicating that the family may not be able to comply with protocol procedures and recommended medical care and follow-up. * Other conditions which in the opinion of the Principal Investigator and/or co-investigators, contra-indicate the infusion of transduced cells or study participation.