Among people living with HIV (PLWH), heavy alcohol use is associated with many negative health consequences. However, the impacts of heavy alcohol use are not well described for PLWH who use drugs. Thus, we investigated the prevalence and correlates of heavy alcohol use among a cohort of people who use drugs (PWUD) living with HIV in Vancouver, Canada. We accessed data from an ongoing community-recruited prospective cohort of PLWH who use drugs with linked comprehensive HIV clinical monitoring data. We used generalized linear mixed-effects modeling to identify factors longitudinally associated with periods of heavy alcohol use between December 2005 and December 2019. Of the 896 participants included, 291 (32.5%) reported at least one period with heavy alcohol use. Periods of recent incarceration (Adjusted Odds Ratio [AOR] = 1.48, 95% Confidence Interval [CI]: 1.01-2.17), encounters with police (AOR = 1.87, 95% CI: 1.37-2.56), and older age (AOR = 1.05, 95% CI: 1.02-1.07) were positively associated with heavy alcohol use. Engagement in drug or alcohol treatment (AOR = 0.54, 95% CI: 0.42-0.70) and male gender (AOR = 0.46; 95% CI: 0.27-0.78) were negatively associated with heavy alcohol use. We observed that heavy alcohol use was clearly linked to involvement with the criminal justice system. These findings, together with the protective effects of substance use treatment, suggest the need to expand access for drug and alcohol treatment programs overall, and in particular through the criminal justice system to reduce alcohol-related harms among PLWH who use drugs.