Chameleons are arboreal lizards with highly independent, large amplitude eye movements. In response to an approaching threat, a chameleon on a vertical pole moves so as to keep itself away from the threat. In so doing, it shifts between monocular and binocular scanning of the threat and of the environment. We analyzed eye movements in the Common chameleon, Chamaeleo chameleon, during avoidance response for lateralization, that is, asymmetry at the functional/behavioral levels. The chameleons were exposed to a threat, approaching horizontally from clockwise or anti-clockwise directions, and that could be viewed monocularly or binocularly. Our results show three broad patterns of eye use, as determined by durations spent viewing the threat and by frequency of eye shifts. Under binocular viewing, two of the patterns were found to be both side dependent, that is, lateralized and role dependent ("leading" or "following"). However, under monocular viewing, no such lateralization was detected. We discuss these findings in light of the situation not uncommon in vertebrates, of independent eye movements and a high degree of optic nerve decussation and that lateralization may well occur in organisms that are regularly exposed to critical stimuli from all spatial directions. We point to the need of further investigating lateralization at fine behavioral levels.