A large global effort is currently ongoing to develop vaccines against SARS-CoV-2, the causative agent of COVID-19. While there is accumulating evidence on the antibody response against SARS-CoV-2, little is known about the SARS-CoV-2 antigens that are targeted by CD8 T cells. To address this issue, we have analyzed samples from 20 COVID-19 patients for T cell recognition of 500 predicted MHC class I epitopes. CD8 T cell reactivity against SARS-CoV- 2 was common. Remarkably, a substantial fraction of the observed CD8 T cell responses were directed towards the ORF1ab polyprotein 1ab, and these CD8 T cell responses were frequently of a very high magnitude. The fact that a major part of the SARS-CoV-2 specific CD8 T cell response is directed against a part of the viral genome that is not included in the majority of vaccine candidates currently in development may potentially influence their clinical activity and toxicity profile.