We studied the prevalent cytotoxic CD8 T cell response mounted against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) Spike glycoprotein269-277 epitope (sequence YLQPRTFLL) via the most frequent human leukocyte antigen (HLA) class I worldwide, HLA A∗02. The Spike P272L mutation that has arisen in at least 112 different SARS-CoV-2 lineages to date, including in lineages classified as "variants of concern," was not recognized by the large CD8 T cell response seen across cohorts of HLA A∗02+ convalescent patients and individuals vaccinated against SARS-CoV-2, despite these responses comprising of over 175 different individual T cell receptors. Viral escape at prevalent T cell epitopes restricted by high frequency HLAs may be particularly problematic when vaccine immunity is focused on a single protein such as SARS-CoV-2 Spike, providing a strong argument for inclusion of multiple viral proteins in next generation vaccines and highlighting the need for monitoring T cell escape in new SARS-CoV-2 variants.