Humans operate with a "theory of mind" with which they are able to understand that others' actions are driven not by reality but by beliefs about reality, even when those beliefs are false. Although great apes share with humans many social-cognitive skills, they have repeatedly failed experimental tests of such false-belief understanding. We use an anticipatory looking test (originally developed for human infants) to show that three species of great apes reliably look in anticipation of an agent acting on a location where he falsely believes an object to be, even though the apes themselves know that the object is no longer there. Our results suggest that great apes also operate, at least on an implicit level, with an understanding of false beliefs.