In a recent Science article, Fitch and Hauser (2004; hereafter, F&H) claimed to have demonstrated that cotton-top tamarins fail to learn an artificial language produced by a phrase structure grammar (Chomsky, 1957) generating center-embedded sentences, whereas adult humans easily learn such a language. We report an experiment replicating the results of F&H in humans but also showing that subjects learned the language without exploiting in any way the center-embedded structure. When the procedure was modified to make the processing of this structure mandatory, the subjects no longer showed evidence of learning. We propose a simple interpretation for the difference in performance observed in F&H's task between humans and tamarins and argue that, beyond the specific drawbacks inherent in F&H's study, researching the source of the inability of nonhuman primates to master language within a framework built around Chomsky's hierarchy of grammars is a conceptual dead end.