The emergence of the COVID-19 outbreak at the end of 2019, caused by the novel coronavirus SARS-CoV-2, has, to date, led to over 13.6 million infections and nearly 600,000 deaths. Consequently, there is an urgent need to better understand the molecular factors triggering immune defense against the virus and to develop countermeasures to hinder its spread. Using in silico analyses, we showed that human major histocompatibility complex (MHC) class I cell-surface molecules vary in their capacity for binding different SARS-CoV-2-derived epitopes, i.e., short sequences of 8-11 amino acids, and pinpointed five specific SARS-CoV-2 epitopes that are likely to be presented to cytotoxic T-cells and hence activate immune responses. The identified epitopes, each one of nine amino acids, have high sequence similarity to the equivalent epitopes of SARS-CoV virus, which are known to elicit an effective T cell response in vitro. Moreover, we give a structural explanation for the binding of SARS-CoV-2-epitopes to MHC molecules. Our data can help us to better understand the differences in outcomes of COVID-19 patients and may aid the development of vaccines against SARS-CoV-2 and possible future outbreaks of novel coronaviruses.