In colour-grapheme synesthesia, non-coloured graphemes are perceived as being inherently coloured. In recent years, it is debated whether visual processing of synesthesia-inducing achromatic graphemes is similar to that of chromatic graphemes. Here, we exploit the phenomenon of binocular rivalry in which incompatible images presented dichoptically compete for conscious expression. Importantly, the competition only arises if the two images are sufficiently different; if the difference between the images is small, the images will fuse into a single mixed percept. We show that achromatic digits that induce synesthetic colour percepts increase the incidence of binocular rivalry compared to achromatic non-digits that do not evoke such percepts. That is, compared to achromatically perceived non-digits, synesthesia-inducing digits increase the predominance of binocular rivalry over binocular fusion. This finding shows that the synesthetic colour experience can provide the conditions for promoting binocular rivalry, much like stimulus features that induce rivalry in normal vision.