Whenever we open our eyes, our brain quickly integrates the two eyes' perspectives into a combined view. This process of binocular integration happens so rapidly that even incompatible stimuli are briefly fused before one eye's view is suppressed in favor of the other (binocular rivalry). The neuronal basis for this brief period of fusion during incompatible binocular stimulation is unclear. Neuroanatomically, the eyes provide two largely separate streams of information that are integrated into a binocular response by the primary visual cortex (V1). However, the temporal dynamics underlying the formation of this binocular response are largely unknown. To address this question, we examined the temporal profile of binocular responses in V1 of fixating monkeys. We found that V1 processes binocular stimuli in a dynamic sequence that comprises at least two distinct temporal phases. An initial transient phase is characterized by enhanced spiking responses for both compatible and incompatible binocular stimuli compared to monocular stimulation. This transient is followed by a sustained response that differed markedly between congruent and incongruent binocular stimulation. Specifically, incompatible binocular stimulation resulted in overall response reduction relative to monocular stimulation (binocular suppression). In contrast, responses to compatible stimuli were either suppressed or enhanced (binocular facilitation) depending on the neurons' ocularity (selectivity for one eye over the other) and laminar location. These results suggest that binocular integration in V1 occurs in at least two sequential steps that comprise initial additive combination of the two eyes' signals followed by widespread differentiation between binocular concordance and discordance.