The primary goal of this study is to evaluate whether intermittent theta burst stimulation (iTBS) is effective for treating depression in people who have depression and chronic hoarding disorder (HD). The study will also evaluate whether this treatment can improve HD symptoms, cognitive performance, and brain region connectivity. The study team will investigate how the treatment works for depression, as well as other factors that can enhance or hinder treatment, such as pre-treatment level of depression, cognitive performance, or brain region connectivity.