The problems of shape classification and part segmentation from 3D point clouds have garnered increasing attention in the last few years. But both of these problems suffer from relatively small training sets, creating the need for statistically efficient methods to learn 3D shape representations. In this work, we investigate the use of Approximate Convex Decompositions (ACD) as a self-supervisory signal for label-efficient learning of point cloud representations. We show that using the results of ACD to approximate a ground truth segmentation provides excellent self-supervision for learning 3D point cloud representations that are highly effective on downstream tasks. We report improvements over the state-of-the art in unsupervised representation learning on the ModelNet40 shape classification dataset and significant gains in few-shot part segmentation on the ShapeNetPart dataset.