A salient visual stimulus can be rendered invisible by presenting it to one eye while flashing a mask to the other eye. This procedure, called continuous flash suppression (CFS), has been proposed as an ideal way of studying awareness as it can make a stimulus imperceptible for extended periods of time. Previous studies have reported robust suppression of cortical activity in higher visual areas during CFS, but the role of primary visual cortex (V1) is still controversial. In this study, we resolve this controversy on the role of V1 in CFS and also begin characterizing the computational processes underlying CFS. Early visual cortical activity was measured with functional magnetic resonance imaging while human subjects viewed stimuli composed of target and mask, presented to the same or different eyes. Functional MRI responses in early visual cortex were smaller when target and mask were in different eyes compared with the same eye, not only for the lowest contrast target rendered invisible by CFS, but also for higher contrast targets, which were visible even when presented to the eye opposite the mask. We infer that CFS is based on modulating the gain of neural responses, akin to reducing target contrast.