The pathogenesis of HIV-1 infection is governed by a highly dynamic, time-dependent interaction between the host and the viral genome. In this study, we developed a novel systematic approach to assess the host-virus interaction, using average pairwise viral diversity as a proxy for time since infection, and applied this method to nearly whole viral genome sequences (n = 4,464), human leukocyte antigen (HLA) genotyping data (n = 1,044), and viral RNA load (VL) measurements during the untreated chronic phase (n = 829) of Swiss HIV Cohort Study participants. Our systematic genome-wide screen revealed for 98 HLA/viral-variant pairs a signature of immune-driven selection in the form of an HLA-dependent effect of infection time on the presence of HIV amino acid variants. Of these pairs, 12 were found to have an effect on VL. Furthermore, 28/58 pairs were validated by time-to-event analyses and 48/92 by computational HLA-epitope predictions. Our diversity-based approach allows a powerful and systematic investigation of the interaction between the virus and cellular immunity, revealing a notable subset of such interaction effects. From an evolutionary perspective, these observations underscore the complexity of HLA-mediated selection pressures on the virus that shape viral evolution and pathogenesis. The intricate interplay between viruses and the human immune system is reflected in dynamic associations between the viral and the human genomes. These often take the form of escape dynamics, in which the virus acquires mutations that allow it to evade immune recognition. We developed a novel viral diversity-based method to screen for such interactions across the viral genome systematically and applied it to a unique dataset of HIV-1 sequences and human leukocyte antigen (HLA) variants. We could identify time-dependent interactions between 98 pairs of HLA and viral variants. Among these pairs, 12 were associated with the concentration of viral RNA, longitudinal time-to-event analyses confirmed 28, and 48 were consistent with computational predictions of viral peptide binding to HLA molecules. Our results highlight how the highly dynamic interaction between the viral genome and the immune system shapes viral evolution, and our approach offers new opportunities to systematically study such interactions from real-world cross-sectional data.