Reduced vigilance is the conspicuous cost of sleep in most animals. To mitigate against this cost, some birds and aquatic mammals have evolved the ability to sleep with one-half of their brain at a time, a phenomenon known as unihemispheric sleep. During unihemispheric sleep the eye neurologically connected to the 'awake' hemisphere remains open while the other eye is closed. Such unilateral eye closure (UEC) has been observed across avian and non-avian reptiles, but has received little attention in the latter. Here, we explored the use of UEC in juvenile saltwater crocodiles (1) under baseline conditions, and in the presence of (2) other young crocodiles and (3) a human. Crocodiles increased the amount of UEC in response to the human, and preferentially oriented their open eye towards both stimuli. These results are consistent with observations on unihemispherically sleeping cetaceans and birds, and could have implications for our understanding of the evolution of unihemispheric sleep.