Aquatic mammals (i.e., Cetaceans, eared seals and manatees) and birds show interhemispheric asymmetries (IA) in slow-wave sleep-related electroencephalographic (EEG) activity, suggesting that the depth of sleep differs between hemispheres. In birds, an association between unilateral eye closure and IA has been reported in five species from three orders (i.e., Galliformes, Charadriiformes, and Anseriformes). Moreover, unilateral eye closure has been observed during behaviorally defined sleep in 29 species from 13 avian orders, suggesting that birds in general display IA during sleep. Despite the apparent prevalence of unilateral eye closure and IA in birds, previous work did not detect IA in the pigeon, thereby challenging the conclusion that this is a general feature of birds. Using digital period amplitude analysis, an objective method for quantifying EEG power (a measure of wave amplitude) across different frequencies, we demonstrate that pigeons do, in fact, display an association between unilateral eye closure and IA. For a given hemisphere, standardized 2–4 Hz EEG power was greater when the contralateral eye was closed when compared to open. We also found that pigeons used the open eye during IA to monitor their environment. In addition, individual pigeons showed a bias for keeping one eye open more than the other. The direction (left vs. right) of this bias differed across birds, and appeared to be influenced by the structure of the surrounding environment. Finally, with the addition of pigeons (order Columbiformes), IA associated with unilateral eye closure has been recorded in four avian orders, suggesting that this form of sleep is widespread in birds.