T cell receptor (TCR)α and β chains cooperatively recognize peptide-MHC (pMHC) complexes. It has been shown that a ‘chain-centric’ TCR hemichain can, by itself, dictate MHC-restricted antigen specificity without requiring major contributions from the paired TCR counterchain. Little is known, however, regarding the relative contributions and roles of chain-centric and its counter, non-chain-centric hemichains in determining T cell avidity. We comprehensively analyzed a thymically unselected T cell repertoire generated by transducing the α chain-centric HLA-A*02:01(A2)/MART127–35 TCRα, clone SIG35α, into A2-matched and unmatched post-thymic T cells. Regardless of their HLA-A2 positivity, a substantial subset of peripheral T cells transduced with SIG35α gained reactivity for A2/MART127–35. While the generated A2/MART127–35-specific T cells used various TRBV genes, TRBV27 predominated with >102 highly diverse and unique clonotypic CDR3β sequences. T cells individually reconstituted with various A2/MART127–35 TRBV27 TCRβ genes along with SIG35α possessed a wide range (>2 log orders) of avidity. Approximately half possessed avidity higher than T cells expressing clone DMF5, a naturally occurring A2/MART127–35 TCR with one of the highest affinities. Importantly, similar findings were recapitulated with other self-antigens. Our results indicate that, although a chain-centric TCR hemichain determines antigen specificity, the paired counterchain can regulate avidity over a broad range (>2 log orders) without compromising antigen specificity. TCR chain centricity can be exploited to generate a thymically unselected antigen-specific T cell repertoire, which can be used to isolate high avidity antitumor T cells and their uniquely encoded TCRs rarely found in the periphery due to tolerance.