Shape completion aims to recover the full 3D geometry of an object from a partial observation. This problem is inherently multi-modal since there can be many ways to plausibly complete the missing regions of a shape. Such diversity would be indicative of the underlying uncertainty of the shape and could be preferable for downstream tasks such as planning. In this paper, we propose a novel conditional generative adversarial network that can produce many diverse plausible completions of a partially observed point cloud. To enable our network to produce multiple completions for the same partial input, we introduce stochasticity into our network via style modulation. By extracting style codes from complete shapes during training, and learning a distribution over them, our style codes can explicitly carry shape category information leading to better completions. We further introduce diversity penalties and discriminators at multiple scales to prevent conditional mode collapse and to train without the need for multiple ground truth completions for each partial input. Evaluations across several synthetic and real datasets demonstrate that our method achieves significant improvements in respecting the partial observations while obtaining greater diversity in completions.