Inclusion Criteria: 1. RAG1-deficient SCID as confirmed by genetic analysis 2. Peripheral blood CD3+T cells \< 300/μL 3. Absence of peripheral blood naïve CD4+ T cells 4. Age \< 2 years 5. Age at least 8 weeks by the time of busulfan and fludarabine administration 6. Lack of an available HLA-identical sibling/family donor 7. Signed informed consent (parental or guardian) 8. Able to return to the local HSCT centre for follow-up (per protocol) during the 5-year trial and up to at least 15-year long-term follow-up after IMP administration Exclusion Criteria: 1. Omenn syndrome 2. Previous allogeneic HSCT 3. 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 4. 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. 5. Human immunodeficiency virus (HIV) infection or Human T-cell Leukemia Virus (HTLV) infection