To examine great apes' on-line prediction of other individuals' actions, we used an eye-tracking technique and an experimental paradigm previously used to test human infants. Twenty-two great apes, including bonobos, chimpanzees, and orangutans, were familiarized to movie clips of a human hand reaching to grasp one of two objects. Then the objects' locations were swapped, and in the test event, the hand made an incomplete reach between the objects. In a control condition, a mechanical claw performed the same actions. The apes predictively looked at the familiarized goal object rather than the familiarized location when viewing the hand action in the test event. However, they made no prediction when viewing the claw action. These results are similar to those reported previously for human infants, and predictive looking did not differ among the three species of great apes. Thus, great apes make on-line goal-based predictions about the actions of other individuals; this skill is not unique to humans but is shared more widely among primates.