We present a scalable framework to learn part segmentation from object instance labels. State-of-the-art instance segmentation models contain a surprising amount of part information. However, much of this information is hidden from plain view. For each object instance, the part information is noisy, inconsistent, and incomplete. PartDistillation transfers the part information of an instance segmentation model into a part segmentation model through self-supervised self-training on a large dataset. The resulting segmentation model is robust, accurate, and generalizes well. We evaluate the model on various part segmentation datasets. Our model outperforms supervised part segmentation in zero-shot generalization performance by a large margin. Our model outperforms when finetuned on target datasets compared to supervised counterpart and other baselines especially in few-shot regime. Finally, our model provides a wider coverage of rare parts when evaluated over 10K object classes. Code is at https://github.com/facebookresearch/PartDistillation.