When dissimilar images are presented to the two eyes, they compete for perceptual dominance so that each image is visible in turn for a few seconds while the other is suppressed. Such binocular rivalry is associated with relative suppression of local, eye-based representations that can also be modulated by high-level influences such as perceptual grouping. However, it is currently unclear how early in visual processing the suppression of eye-based signals can occur. Here we use high-resolution functional magnetic resonance imaging (fMRI) in conjunction with a new binocular rivalry stimulus to show that signals recorded from the human lateral geniculate nucleus (LGN) exhibit eye-specific suppression during rivalry. Regions of the LGN that show strong eye-preference independently show strongly reduced activity during binocular rivalry when the stimulus presented in their preferred eye is perceptually suppressed. The human LGN is thus the earliest stage of visual processing that reflects eye-specific dominance and suppression.