Shape completion is the problem of completing partial input shapes such as partial scans. This problem finds important applications in computer vision and robotics due to issues such as occlusion or sparsity in real-world data. However, most of the existing research related to shape completion has been focused on completing shapes by learning a one-to-one mapping which limits the diversity and creativity of the produced results. We propose a novel multimodal shape completion technique that is effectively able to learn a one-to-many mapping and generates diverse complete shapes. Our approach is based on the conditional Implicit Maximum Likelihood Estimation (IMLE) technique wherein we condition our inputs on partial 3D point clouds. We extensively evaluate our approach by comparing it to various baselines both quantitatively and qualitatively. We show that our method is superior to alternatives in terms of completeness and diversity of shapes.