Inclusion Criteria: 1. RAG1-deficient SCID as confirmed by genetic analysis 2. Peripheral blood T cells \< 300/μL and/or naïve T cells \< 1/μL 3. Age \< 2 years 4. Age at least 8 weeks by the time of busulfan and fludarabine administration 5. Lack of an available HLA-matched donor (HLA-identical sibling or 10/10 (A, B, C, DR, DQ) allele-matched (un)related donor) 6. Signed informed consent (parental or guardian) 7. Able to return to the study centre for follow-up (per protocol) during the 2-year study and the 15-year long-term off study review Exclusion Criteria: 1. Availability of an HLA-matched donor (HLA-identical sibling or 10/10 (A, B, C, DR, DQ) allele-matched (un)related donor) 2. RAG1 deficiency with peripheral blood T cells \> 300/μL and/or naïve T cells \> 1/μL 3. Omenn syndrome 4. Previous allogeneic HSCT 5. Significant organ dysfunction/co-morbidity (including but not limited to the ones listed below): 1. Mechanical ventilation 2. Shortening fraction on echocardiogram \<25% 3. Renal failure defined as dialysis dependence 4. Uncontrolled seizure disorder 6. Any other condition that the investigator considers is a contraindication to collection and/or infusion of trans-duced cells for that individual or indicate patient's inability to follow the protocol, for example contraindication f to busulfan, major congenital abnormalities, ineligible to receive anaesthesia, or documented refusal or inability of the family to return for scheduled visits. 7. Human immunodeficiency virus (HIV) infection or Human T-cell Leukemia Virus (HTLV) infection