Transferring the style from one image onto another is a popular and widely studied task in computer vision. Yet, learning-based style transfer in the 3D setting remains a largely unexplored problem. To our knowledge, we propose the first learning-based generative approach for style transfer between 3D objects. Our method allows to combine the content and style of a source and target 3D model to generate a novel shape that resembles in style the target while retaining the source content. The proposed framework can synthesize new 3D shapes both in the form of point clouds and meshes. Furthermore, we extend our technique to implicitly learn the underlying multimodal style distribution of the individual category domains. By sampling style codes from the learned distributions, we increase the variety of styles that our model can confer to a given reference object. Experimental results validate the effectiveness of the proposed 3D style transfer method on a number of benchmarks.