When the two eyes view discrepant monocular stimuli, stable single vision gives way to alternating periods of monocular dominance; this is the well-known but little understood phenomenon of binocular rivalry. This article develops a neural theory of binocular rivalry that treats the phenomenon as the default outcome when binocular correspondence cannot be established. The theory posits the existence of monocular and binocular neurons arrayed within a functional processing module, with monocular neurons playing a crucial role in signaling the stimulus conditions instigating rivalry and generating inhibitory signals to implement suppression. Suppression is conceived as a local process happening in parallel over the entire cortical representation of the binocular visual field. The strength of inhibition causing suppression is related to the size of the pool of monocular neurons innervated by the suppressed eye, and the duration of a suppression phase is attributed to the strength of excitation generated by the suppressed stimulus. The theory is compared with three other contemporary theories of binocular rivalry. The article closes with a discussion of some of the unresolved problems related to the theory.