V(D)J recombination is one of the most complex DNA transactions in biology. The RAG complex makes double-stranded breaks adjacent to signal sequences and creates hairpin coding ends. Here, we find that the kinase activity of the Artemis:DNA-PKcs complex can be activated by hairpin DNA ends in cis, thereby allowing the hairpins to be nicked and then to undergo processing and joining by nonhomologous DNA end joining. Based on these insights, we have reconstituted many aspects of the antigen receptor diversification of V(D)J recombination by using 13 highly purified polypeptides, thereby permitting variable domain exon assembly by using this fully defined system in accord with the 12/23 rule for this process. The features of the recombination sites created by this system include all of the features observed in vivo (nucleolytic resection, P nucleotides, and N nucleotide addition), indicating that most, if not all, of the end modification enzymes have been identified.