Tasks that tax working memory (WM) have consistently been found to decrease mind wandering. These findings may indicate that maintenance of mind wandering requires WM resources, such that mind wandering cannot persist when WM resources are being consumed by a task. An alternative explanation for these findings, however, is that mind wandering persists without the support of WM but is nonetheless decreased during any demanding task because good task performance requires that attention be restricted from task-unrelated thought (TUT). The present study tested these two competing theories by investigating whether individuals with greater WM resources mind-wander more during an undemanding task, as would be predicted only by the theory that WM supports TUT. We found that individuals with higher WM capacity reported more TUT in undemanding tasks, which suggests that WM enables the maintenance of mind wandering.