Although chimpanzees understand what others may see, it is unclear whether they understand how others see things (Level 2 perspective-taking). We investigated whether chimpanzees can predict the behavior of a conspecific which is holding a mistaken perspective that differs from their own. The subject competed with a conspecific over two food sticks. While the subject could see that both were the same size, to the competitor one appeared bigger than the other. In a previously established game, the competitor chose one stick in private first and the subject chose thereafter, without knowing which of the sticks was gone. Chimpanzees and 6-year-old children chose the 'riskier' stick (that looked bigger to the competitor) significantly less in the game than in a nonsocial control. Children chose randomly in the control, thus showing Level 2 perspective-taking skills; in contrast, chimpanzees had a preference for the 'riskier' stick here, rendering it possible that they attributed their own preference to the competitor to predict her choice. We thus run a follow-up in which chimpanzees did not have a preference in the control. Now, they also chose randomly in the game. We conclude that chimpanzees solved the task by attributing their own preference to the other, while children truly understood the other's mistaken perspective.