There are no FDA approved treatments for use in adults with autism spectrum disorder (ASD), many of whom have distressing anxiety, mood disturbances, sleep problems, and agitation. Some researchers and individuals with ASD have noted that cannabidiol (CBD) is beneficial for those psychiatric problems. This study is to learn more about the effectiveness and safety of CBD in the treatment of psychiatric problems in adults with ASD. The study will last 14 weeks total, during which six weeks participants will receive a pill containing CBD, two weeks where participants will receive no drug/placebo, and six weeks where participants will receive the placebo, an inactive pill. As part of the study, participants will have regular visits and be asked questions about anxiety, challenging behaviors, daily functioning, cognition, and physical symptoms, on standard assessments.