In industrial part kitting, 3D objects are inserted into cavities for transportation or subsequent assembly. Kitting is a critical step as it can decrease downstream processing and handling times and enable lower storage and shipping costs. 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 dataaugmentation to train a convolutional neural network (CNN) to robustly estimate 3D rotations between objects and matching concave or convex cavities using a large training dataset of simulated depth images 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 98.9 % average intersection volume between the object mesh and that of the target cavity. Physical experiments with industrial objects succeed in 18 % of trials using a baseline method and in 63 % of trials with Kit-Net. Video, code, and data are available at https://github.com/BerkeleyAutomation/Kit-Net.