Previous research has shown that the right hemisphere processes low spatial frequencies more efficiently than the left hemisphere, which preferentially processes high spatial frequencies. These studies have typically measured RTs to single, briefly flashed gratings and/or have directed observers to attend to a particular spatial frequency immediately before making a judgment about a subsequently presented stimulus. Thus, it is unclear whether the hemispheres differ in perceptual selection from multiple spatial frequencies that are simultaneously present in the environment, without bias from selective attention. Moreover, the time course of hemispheric asymmetry in spatial frequency processing is unknown. We addressed both of these questions with binocular rivalry, a measure of perceptual selection from competing alternatives over time. Participants viewed a pair of rivalrous orthogonal gratings with different spatial frequencies, presented either to the left or right of central fixation, and continuously reported which grating they perceived. At the beginning of a trial, the low spatial frequency grating was perceptually selected more often when presented in the left hemifield (right hemisphere) than in the right hemifield (left hemisphere), whereas the high spatial frequency grating showed the opposite pattern of results. This hemispheric asymmetry in perceptual selection persisted for the entire 30-sec stimulus presentation, continuing long after stimulus onset. These results indicate stable differences in the resolution of ambiguity across spatial locations and demonstrate the importance of considering sustained differences in perceptual selection across space when characterizing conscious representations of complex scenes.