In most environments, the visual system is confronted with many relevant objects simultaneously. This is especially true during reading. However, recent behavioral experiments demonstrate that a fundamental processing bottleneck prevents recognition of more than one word at a time (White, Palmer & Boynton, Psychological Science 2018). Here, we used functional magnetic resonance imaging (fMRI) to investigate the neuronal basis of that bottleneck. Fifteen observers viewed masked pairs of words (one on either side of fixation) and performed a semantic categorization task during fMRI scanning. On each trial they were cued to attend selectively to the right word or the left word, or to divide attention between both words. Responses in retinotopic visual cortex were consistent with unlimited capacity parallel processing: the two words were processed by parallel spatial channels, one in each contralateral hemisphere. Responses were higher to attended words than ignored words, but were not reduced when attention was divided, although behavioral performance suffered greatly. We then analyzed responses in word-selective patches of ventral occipito-temporal cortex, which have been termed the “visual word form area(s)”. A relatively posterior patch in the left hemisphere responded to words on both sides of fixation but nonetheless, and quite surprisingly, appeared to process them in two spatial channels that can be independently modulated by spatial attention. Therefore, like retinotopic cortex, this area also supports parallel processing prior to the bottleneck. In contrast, a more anterior word-selective region in the left hemisphere showed no spatial or attentional selectivity, consistent with processing after the bottleneck. Our interpretation is that the visual system can process two words in parallel up to a relatively late stage in the ventral stream. Beyond this point there are no longer separable neural populations for the two words, leading to behavioral deficits when dividing attention between words.