T cell receptors (TCRs) are formed by stochastic gene rearrangements, theoretically generating >1019 sequences. They are selected during thymopoiesis, which releases a repertoire of about 108 unique TCRs per individual. How evolution shaped a process that produces TCRs that can effectively handle a countless and evolving set of infectious agents is a central question of immunology. The paradigm is that a diverse enough repertoire of TCRs should always provide a proper, though rare, specificity for any given need. Expansion of such rare T cells would provide enough fighters for an effective immune response and enough antigen-experienced cells for memory. We show here that human thymopoiesis releases a large population of CD8+ T cells harboring α/β paired TCRs that (i) have high generation probabilities and (ii) a preferential usage of some V and J genes, (iii) are shared between individuals and (iv) can each recognize and be activated by multiple unrelated viral peptides, notably from EBV, CMV and influenza. These polyspecific T cells may represent a first line of defense that is mobilized in response to infections before a more specific response subsequently ensures viral elimination. Our results support an evolutionary selection of polyspecific α/β TCRs for broad antiviral responses and heterologous immunity.