Advanced age is associated with severe symptoms and death upon SARS-CoV-2 infection. Virus-specific CD8⁺ T-cell responses have shown to be protective toward critical COVID-19 manifestations, suggesting that suboptimal cellular immunity may contribute to the age-pattern of the disease. The induction of a CD8⁺ T-cell response against an emerging pathogen like SARS-CoV-2 relies on the activation of naive T cells. To investigate whether the primary CD8⁺ T-cell response against this virus is defective in advanced age, we used an in vitro approach to prime SARS-CoV-2-specific naive CD8⁺ T cells from healthy, unexposed donors of different age groups. Compared to younger adults, older individuals display a poor SARS-CoV-2-specific T-cell priming capacity in terms of both magnitude and quality of the response. In addition, older subjects recognize a lower number of epitopes. Our results implicate that immune aging is associated with altered primary SARS-CoV-2-specific CD8⁺ T-cell responses.