Lateralisation of eye use indicates differential specialisation of the brain hemispheres. We tested eye use by zebra finches to view a model predator, a monitor lizard, and compared this to eye use to view a non-threatening visual stimulus, a jar. We used a modified method of scoring eye preference of zebra finches, since they often alternate fixation of a stimulus with the lateral, monocular visual field of one eye and then the other, known as biocular alternating fixation. We found a significant and consistent preference to view the lizard using the left lateral visual field, and no significant eye preference to view the jar. This finding is consistent with specialisation of the left eye system, and right hemisphere, to attend and respond to predators, as found in two other avian species and also in non-avian vertebrates. Our results were considered together with hemispheric differences in the zebra finch for processing, producing, and learning song, and with evidence of right-eye preference in visual searching and courtship behaviour. We conclude that the zebra finch brain has the same general pattern of asymmetry for visual processing as found in other vertebrates and suggest that, contrary to earlier indications from research on lateralisation of song, this may also be the case for auditory processing.