We describe a physics-based learning model for predicting the immunogenicity of Cytotoxic T Lymphocyte (CTL) epitopes derived from diverse pathogens, given a Human Leukocyte Antigen (HLA) genotype. The model was trained and tested on experimental data on the relative immunodominance of CTL epitopes in Human Immunodeficiency Virus infection. The method is more accurate than publicly available models. Our model predicts that only a fraction of SARS-CoV-2 epitopes that have been predicted to bind to HLA molecules is immunogenic. The immunogenic CTL epitopes across all SARS-CoV-2 proteins are predicted to provide broad population coverage, but the immunogenic epitopes in the SARS-CoV-2 spike protein alone are unlikely to do so. Our model predicts that several immunogenic SARS-CoV-2 CTL epitopes are identical to those contained in low-pathogenicity coronaviruses circulating in the population. Thus, we suggest that some level of CTL immunity against COVID-19 may be present in some individuals prior to SARS-CoV-2 infection.