We present Kit-Net, a framework for kitting previously unseen 3D objects into cavities given depth images of both the target cavity and an object held by a gripper in an unknown initial orientation. Kit-Net uses self-supervised deep learning and data-augmentation to train a Convolutional Neural Network (CNN) to robustly estimate 3D rotations between objects and matching concave or convex cavities using a large dataset of simulated depth image pairs. Kit-Net then uses the trained CNN to implement a controller to orient and position novel objects for insertion into novel prismatic and conformal 3D cavities. Experiments in simulation suggest that Kit-Net can orient objects to have a 99% average intersection volume between the object mesh and that of the target cavity. Physical experiments with 3 industrial objects suggest that Kit-Net can successfully insert objects into cavities with a 63% success rate while a baseline which restricts itself to 2D rotations succeeds only 18% of the time.