Elucidating antiviral CD8 T lymphocyte responses to SARS-CoV-2 may shed light on the heterogeneity of clinical outcomes and inform vaccine or therapeutic approaches. To facilitate the evaluation of antiviral CD8 T cell responses to SARS-CoV-2, we generated a publicly accessible database of epitopes predicted to bind any class I HLA protein across the entire SARS-CoV-2 proteome. While a subset of epitopes from earlier betacoronaviruses, such as SARS-CoV (SARS), have been validated experimentally, validation systems are often biased toward specific HLA haplotypes (notably HLA-A*02:01) that only account for a fraction of the haplotypes of individuals affected by the SARS-CoV-2 pandemic. To enable evaluation of epitopes across individuals with a variety of HLA haplotypes, we computed the predicted binding affinities between 9-mer peptides derived from the annotated SARS-CoV-2 peptidome across 9,360 MHC class I HLA-A, -B, and -C alleles. There were 6,748 unique combinations of peptides and HLA alleles (pMHCs) with a predicted binding affinity of less than 500nM, including 1,103 unique peptides and 1,022 HLA alleles, spanning 11 annotated superfamilies. These peptides were derived from all 11 proteins spanning the SARS-CoV-2 peptidome, including peptides that have previously been validated experimentally. We also show evidence that these previously validated epitopes may be relevant in other HLA contexts. This complete dataset is available publicly: gs://pici-covid19-data-resources/mhci/peptide_predictions.