Defining the ontogeny of the human adaptive immune system during embryogenesis has implications for understanding childhood diseases including leukemias and autoimmune conditions. Using RAG1:GFP human pluripotent stem cell (PSC) reporter lines, we examined human T-cell genesis from PSC derived hematopoietic organoids. Under conditions favouring T-cell development, RAG1+ cells progressively up regulated a cohort of recognised T-cell associated genes, arresting development at the CD4+CD8+ stage. Sort and re-culture experiments showed that early RAG1+ cells also possessed B-cell, myeloid and erythroid potential, with B-cell potential correlating with co-expression of the progenitor marker VECAD. Consistent with this, RNAseq analysis of the early RAG1+ cells indicated that, in addition to T-lineage genes, this population expressed genes associated with erythroid and myeloid lineages. In addition, flow cytometry and single cell RNA sequencing data showed that early RAG1+ cells co-expressed the endothelial/hematopoietic progenitor markers CD34, VECAD and CD90 whilst imaging studies identified RAG1+ cells within CD31+ endothelial structures that co-expressed SOX17+ or the endothelial marker, CAV1. Collectively, these observations provide evidence for a wave of human T-cell development that originates directly from haemogenic endothelium via a RAG1+ intermediate with multi-lineage potential.