If subjects are taught to match Stimulus A to B and then, without further training, match B to A, they have passed a test of symmetry. It has been suggested that non-humans' lack of success on symmetry tests might be overcome by giving them a history of symmetry exemplar training, that is, by directly teaching a large number of conditional relations (e.g., AB, CD, EF,...) and also directly training the "reverse" of these relations (e.g., BA, DC, FE,...). The chimpanzee subjects of the present study, Sherman, Austin, and Lana, had already received extensive symmetry exemplar training as a result of attempts to teach a selection-based language system of lexigrams. The present study systematically subjected 2 of these chimps (Sherman and Lana), for the first time, to standard symmetry tests in controlled conditions. Both chimps failed the tests, even when their correct responses on test trials were reinforced. The findings do not support the exemplar training hypothesis, and cast doubt upon whether the chimps can pass tests of stimulus equivalence.