This project aims to determine whether cannabidiol (CBD), a compound derived from the cannabis plant, is effective in treating alcohol use disorder (AUD) in individuals with comorbid posttraumatic stress disorder (PTSD). Investigators will test the hypothesis that oral cannabidiol (CBD) will reduce alcohol drinking in individuals with AUD comorbid with PTSD. To test this hypothesis, 50 otherwise healthy adult participants with moderate or severe AUD and PTSD will be randomized to treatment with either CBD (400 mg daily) or placebo, for a period of 6 weeks, such that both participants and study staff are blind to treatment condition. Participants (each treated for 6 weeks) will be continuously recruited over a study period of 14 months until 50 have completed. Baseline and weekly data will be collected on alcohol usage and PTSD symptoms, and investigators will assess whether CBD treatment leads to a greater improvement in these measures relative to placebo, and whether reduction in alcohol drinking is temporally linked to improvement in PTSD symptoms. Subjects will also participate in a task designed to quantify the psychological and physiological links between negative emotion produced by re-experiencing PTSD trauma, and alcohol craving. The task will be administered at baseline, before treatment, and following 6 weeks of treatment. Treatment-associated reduction in alcohol craving elicited by trauma-associated negative emotion between CBD and placebo groups will be compared. This study will be the first to test whether CBD is effective in treating alcohol addiction and in treating PTSD in humans, and the first to examine the interaction between these treatment effects. Results will serve as proof of concept and provide guidance for a future larger clinical trial. Because CBD is a safe, readily available drug, such a trial would have an immense potential to prevent death, medical illness, and psychological suffering associated with AUD and PTSD. Further, because the brain circuits via which CBD acts to produce hypothesized effects are relatively well-understood, results may substantially advance understanding of the neurobiological basis of alcohol addiction.