The occipital face area (OFA) and fusiform face area (FFA) are brain regions thought to be specialized for face perception. However, their intrinsic functional organization and status as cortical areas with well-defined boundaries remains unclear. Here we test these regions for “faciotopy”, a particular hypothesis about their intrinsic functional organisation. A faciotopic area would contain a face-feature map on the cortical surface, where cortical patches represent face features and neighbouring patches represent features that are physically neighbouring in a face. The faciotopy hypothesis is motivated by the idea that face regions might develop from a retinotopic protomap and acquire their selectivity for face features through natural visual experience. Faces have a prototypical configuration of features, are usually perceived in a canonical upright orientation, and are frequently fixated in particular locations. To test the faciotopy hypothesis, we presented images of isolated face-features at fixation to subjects during functional magnetic resonance imaging. The responses in V1 were best explained by low-level image properties of the stimuli. OFA, and to a lesser degree FFA, showed evidence for a faciotopic organization. When a single patch of cortex was estimated for each face feature, the cortical distances between the feature patches reflected the physical distance between the features in a face. Faciotopy would be the first example, to our knowledge, of a cortical map reflecting the topology, not of a part of the organism itself (its retina in retinotopy, its body in somatotopy), but of an external object of particular perceptual significance.