Introduction: People living with HIV (PLWH) can exhibit impaired immune responses to vaccines. Accumulating evidence indicates that PLWH, particularly those receiving antiretroviral therapy, mount strong antibody responses to COVID-19 vaccination, but fewer studies have examined cellular immune responses to vaccination. We measured SARS-CoV-2 spike-specific CD4+ and CD8+ T cell responses generated by two and three doses of COVID-19 vaccine in PLWH receiving antiretroviral therapy, compared to control participants without HIV. We also quantified T cell responses after post-vaccine breakthrough infection, and receipt of fourth vaccine doses, in a subset of PLWH. Methods: We quantified CD4+ and CD8+ T cells reactive to overlapping peptides spanning the ancestral SARS-CoV-2 spike protein in 50 PLWH and 87 controls without HIV, using an activation induced marker (AIM) assay. All participants remained SARS-CoV-2 naive until at least one month after their third vaccine dose. SARS-CoV-2 infection was determined by seroconversion to nucleocapsid (N) antigen, which occurred in 21 PLWH and 38 controls post-third dose. Multivariable regression analyses were used to investigate relationships between sociodemographic, health and vaccine-related variables and vaccine-induced T cell responses, as well as breakthrough infection risk. Results: A third vaccine dose boosted spike-specific CD4+ and CD8+ T cell frequencies significantly above those measured after the second dose (all p<0.0001). Median T cell frequencies did not differ between PLWH and controls after the second dose (p>0.1), but CD8+ T cell responses were modestly lower in PLWH after the third dose (p=0.02), an observation that remained significant after adjustment for sociodemographic, health and vaccine-related variables (p=0.045). In PLWH who experienced breakthrough infection, median T cell frequencies increased even higher than those observed after three vaccine doses (p<0.03), and CD8+ T cell responses in this group remained higher even after a fourth vaccine dose (p=0.03). In multivariable analysis, the only factor associated with increased breakthrough infection risk was younger age, consistent with the rapid increases in SARS-CoV-2 seropositivity among younger adults in Canada after the initial appearance of the Omicron variant. Conclusion: PLWH receiving antiretroviral therapy mount strong T cell responses to COVID-19 vaccines that can be enhanced by booster doses or breakthrough infection.