There is a persistent methodological problem in primate mindreading research, dubbed the 'logical problem,' over how to determine experimentally whether chimpanzees are mindreaders or just clever behavior-readers of a certain sort. The problem has persisted long enough that some researchers have concluded that it is intractable. The logical problem, I argue, is tractable but only with experimental protocols that are fundamentally different from those that have been currently used or suggested. In the first section, I describe what the logical problem (...) is and how it can, in principle, be solved. In the second section, I illustrate how a well-known experimental protocol by Hare et al. fails to solve the logical problem. In the third section, I do the same for a protocol by Heyes . .) In the fourth section, I describe a novel experimental protocol for visual perspective-taking and argue that it succeeds to discriminate between the relevant mindreading and behavior-reading hypotheses. In addition, this new experimental protocol employs procedures that are realistic enough to suppose that chimpanzees might very well succeed in passing them. (shrink)