Peripheral blood mononuclear cells collected from participants between 2015 - 2018 were stimulated in vitro to identify the capacity of the T cell response in people unexposed to SARS-CoV-2. A total of 142 peptides from SARS-CoV-2 were identified, 66 from the spike protein, which elicited an immune response. Epitopes from the spike antigen most often yielded responses and yielded the most vigorous responses. The ability for T cells in unexposed people to respond to SARS-CoV-2 is likely due to cross-reactivity from memory CD4+ T cells that recognize common cold human coronaviruses (HCoVs). Epitopes from SARS-CoV-2 that demonstrated over 67% homology to corresponding HCoV epitopes were more likely to yield an immune response. These findings contrast with previous studies suggesting HCoV neutralizing antibodies do not demonstrate cross-reactivity to SARS-CoV-2. Cross-reactivity of memory CD4+ T cells has implications for vaccine performance and demonstrates the potential for HCoVs exposure to affect COVID-19 disease severity.