T‐cell destiny during thymic selection depends on the affinity of the TCR for autologous peptide ligands presented in the context of MHC molecules. This is a delicately balanced process; robust binding leads to negative selection, yet some affinity for the antigen complex is required for positive selection. All TCRs of the resulting repertoire thus have some intrinsic affinity for an MHC type presenting an assortment of peptides. Generally, TCR affinities of peripheral T cells will be low toward self‐derived peptides, as these would have been presented during thymic selection, whereas, by serendipity, binding to pathogen‐derived peptides that are encountered de novo could be stronger. A crucial question in assessing immunotherapeutic strategies for cancer is whether natural TCR repertoires have the capacity for efficiently recognizing tumor‐associated peptide antigens. Here, we report a comprehensive comparison of TCR affinities to a range of HLA‐A2 presented antigens. TCRs that bind viral antigens fall within a strikingly higher affinity range than those that bind cancer‐related antigens. This difference may be one of the key explanations for tumor immune escape and for the deficiencies of T‐cell vaccines against cancer.