We propose a method for estimating the 6DoF pose of a rigid object with an available 3D model from a single RGB image. Unlike classical correspondence-based methods which predict 3D object coordinates at pixels of the input image, the proposed method predicts 3D object coordinates at 3D query points sampled in the camera frustum. The move from pixels to 3D points, which is inspired by recent PIFu-style methods for 3D reconstruction, enables reasoning about the whole object, including its (self-)occluded parts. For a 3D query point associated with a pixel-aligned image feature, we train a fully-connected neural network to predict: (i) the corresponding 3D object coordinates, and (ii) the signed distance to the object surface, with the first defined only for query points in the surface vicinity. We call the mapping realized by this network as Neural Correspondence Field. The object pose is then robustly estimated from the predicted 3D-3D correspondences by the Kabsch-RANSAC algorithm. The proposed method achieves state-of-the-art results on three BOP datasets and is shown superior especially in challenging cases with occlusion. The project website is at: linhuang17.github.io/NCF.