The common chameleon, Chamaeleo chameleon, is an arboreal lizard with highly independent, large-amplitude eye movements. In response to a moving threat, a chameleon on a perch responds with distinct avoidance movements that are expressed in its continuous positioning on the side of the perch distal to the threat. We analyzed body-exposure patterns during threat avoidance for evidence of lateralization, that is, asymmetry at the functional/behavioral levels. Chameleons were exposed to a threat approaching horizontally from the left or right, as they held onto a vertical pole that was either wider or narrower than the width of their head, providing, respectively, monocular or binocular viewing of the threat. We found two equal-sized sub-groups, each displaying lateralization of motor responses to a given direction of stimulus approach. Such an anti-symmetrical distribution of lateralization in a population may be indicative of situations in which organisms are regularly exposed to crucial stimuli from all spatial directions. This is because a bimodal distribution of responses to threat in a natural population will reduce the spatial advantage of predators.