Unilateral brain damage can lead to a striking deficit in awareness of stimuli on one side of space called Spatial Neglect. Patient studies show that neglect of the left is markedly more persistent than of the right and that its severity increases under states of low alertness. There have been suggestions that this alertness-spatial awareness link may be detectable in the general population. Here, healthy human volunteers performed an auditory spatial localisation task whilst transitioning in and out of sleep. We show, using independent electroencephalographic measures, that normal drowsiness is linked with a remarkable unidirectional tendency to mislocate left-sided stimuli to the right. The effect may form a useful healthy model of neglect and help in understanding why leftward inattention is disproportionately persistent after brain injury. The results also cast light on marked changes in conscious experience before full sleep onset.