We present 3D CoMPaT, a richly annotated large-scale dataset of more than 7.19 million rendered compositions of Materials on Parts of 7262 unique 3D Models; 990 compositions per model on average. 3D CoMPaT covers 43 shape categories, 235 unique part names, and 167 unique material classes that can be applied to parts of 3D objects. Each object with the applied part-material compositions is rendered from four equally spaced views as well as four randomized views, leading to a total of 58 million renderings (7.19 million compositions × 8 views). This dataset primarily focuses on stylizing 3D shapes at part-level with compatible materials. We introduce a new task, called Grounded CoMPaT Recognition (GCR), to collectively recognize and ground compositions of materials on parts of 3D objects. We present two variations of this task and adapt state-of-art 2D/3D deep learning methods to solve the problem as baselines for future research. We hope our work will help ease future research on compositional 3D Vision. The dataset and code are publicly available at https://www.3dcompat-dataset.org/.