At the core of the binocular rivalry phenomenon lies the spontaneous alternation between the two percepts. Understanding what drives that alternation is a major and key part of understanding the neural basis of binocular rivalry. A starting point in this direction is to characterize the factors that determine the rivalry alternation rate. It is known that some stimulus factors (e.g., contrast) can influence the rate of rivalry, here we tested whether stimuli projected to different parts of the cortex have different rivalry rates. Is there a visual field asymmetry of the rivalry dynamics? Eight near peripheral locations were tested: two eccentricity levels (1 and 4 degrees) at the four major meridians. A red circular grating and a green radius grating were dichoptically presented to the two eyes. Observers were asked to track their perceptual experience by making keypress responses to indicate which of the stimuli came into view. Results from 10 observers (two authors and eight naive observers) show that the alternation rate in binocular rivalry is faster when the stimuli were presented to the right visual field compared to when they were presented to the left visual field. Similarly, rival stimuli in the lower visual field generated faster alternations than that in the upper visual field. There are a number of potential reasons that can lead to the observed rivalry asymmetry. For example, visual attention maybe biased towards the lower and the right visual fields, or at the site of binocular rivalry, the time course of neuronal responses could be faster for information from the lower and right visual fields than that from the upper and left visual fields. In any case, this visual field dependence suggests that the process of binocular rivalry is influenced by retinotopically specific mechanisms.