Point clouds are challenging to process due to their sparsity, therefore autonomous vehicles rely more on appearance attributes than pure geometric features. However, 3D LIDAR perception can provide crucial information for urban navigation in challenging light or weather conditions. In this paper, we investigate the versatility of Shape Completion for 3D Object Tracking in LIDAR point clouds. We design a Siamese tracker that encodes model and candidate shapes into a compact latent representation. We regularize the encoding by enforcing the latent representation to decode into an object model shape. We observe that 3D object tracking and 3D shape completion complement each other. Learning a more meaningful latent representation shows better discriminatory capabilities, leading to improved tracking performance. We test our method on the KITTI Tracking set using car 3D bounding boxes. Our model reaches a 76.94% Success rate and 81.38% Precision for 3D Object Tracking, with the shape completion regularization leading to an improvement of 3% in both metrics.