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The T cell receptor (TCR) repertoire encodes immune exposure history through the dynamic formation of immunological memory. Statistical analysis of repertoire sequencing data has the potential to decode disease associations from large cohorts with measured phenotypes. However, the repertoire perturbation induced by a given immunological challenge is conditioned on genetic background via major histocompatibility complex (MHC) polymorphism. We explore associations between MHC alleles, immune exposures, and shared TCRs in a large human cohort. Using a previously published repertoire sequencing dataset augmented with high-resolution MHC genotyping, our analysis reveals rich structure: striking imprints of common pathogens, clusters of co-occurring TCRs that may represent markers of shared immune exposures, and substantial variations in TCR-MHC association strength across MHC loci. Guided by atomic contacts in solved TCR:peptide-MHC structures, we identify sequence covariation between TCR and MHC. These insights and our analysis framework lay the groundwork for further explorations into TCR diversity.