We present a technique for estimating the relative 3D rotation of an RGB image pair in an extreme setting, where the images have little or no overlap. We observe that, even when images do not overlap, there may be rich hidden cues as to their geometric relationship, such as light source directions, vanishing points, and symmetries present in the scene. We propose a network design that can automatically learn such implicit cues by comparing all pairs of points between the two input images. Our method therefore constructs dense feature correlation volumes and processes these to predict relative 3D rotations. Our predictions are formed over a fine-grained discretization of rotations, bypassing difficulties associated with regressing 3D rotations. We demonstrate our approach on a large variety of extreme RGB image pairs, including indoor and outdoor images captured under different lighting conditions and geographic locations. Our evaluation shows that our model can successfully estimate relative rotations among non-overlapping images without compromising performance over overlapping image pairs.