The rate of progression of HIV infected individuals to AIDS is known to vary with the genotype of the host, and is linked to their allele of human leukocyte antigen (HLA) proteins, which present protein degradation products at the cell surface to circulating T-cells. HLA alleles are associated with Gag-specific T-cell responses that are protective against progression of the disease. While Pol is the most conserved HIV sequence, its association with immune control is not as strong. To gain a more thorough quantitative understanding of the factors that contribute to immunodominance, we have constructed a model of the recognition of HIV infection by the MHC class I pathway. Our model predicts surface presentation of HIV peptides over time, demonstrates the importance of viral protein kinetics, and provides evidence of the importance of Gag peptides in the long-term control of HIV infection. Furthermore, short-term dynamics are also predicted, with simulation of virion-derived peptides suggesting that efficient processing of Gag can lead to a 50% probability of presentation within 3 hours post-infection, as observed experimentally. In conjunction with epitope prediction algorithms, this modelling approach could be used to refine experimental targets for potential T-cell vaccines, both for HIV and other viruses.