Chameleons perform large-amplitude eye movements that are frequently referred to as independent, or disconjugate. When prey (an insect) is detected, the chameleon's eyes converge to view it binocularly and 'lock' in their sockets so that subsequent visual tracking is by head movements. However, the extent of the eyes' independence is unclear. For example, can a chameleon visually track two small targets simultaneously and monocularly, i.e. one with each eye? This is of special interest because eye movements in ectotherms and birds are frequently independent, with optic nerves that are fully decussated and intertectal connections that are not as developed as in mammals. Here, we demonstrate that chameleons presented with two small targets moving in opposite directions can perform simultaneous, smooth, monocular, visual tracking. To our knowledge, this is the first demonstration of such a capacity. The fine patterns of the eye movements in monocular tracking were composed of alternating, longer, 'smooth' phases and abrupt 'step' events, similar to smooth pursuits and saccades. Monocular tracking differed significantly from binocular tracking with respect to both 'smooth' phases and 'step' events. We suggest that in chameleons, eye movements are not simply 'independent'. Rather, at the gross level, eye movements are (i) disconjugate during scanning, (ii) conjugate during binocular tracking and (iii) disconjugate, but coordinated, during monocular tracking. At the fine level, eye movements are disconjugate in all cases. These results support the view that in vertebrates, basic monocular control is under a higher level of regulation that dictates the eyes' level of coordination according to context.