A point cloud is a discrete set of data points sampled from a 3D geometric surface. Chamfer distance (CD) is a popular metric and training loss to measure the distances between point clouds, but also well known to be sensitive to outliers. To address this issue, in this paper we propose InfoCD, a novel contrastive Chamfer distance loss to learn to spread the matched points for better distribution alignments between point clouds as well as accounting for a surface similarity estimator. We show that minimizing InfoCD is equivalent to maximizing a lower bound of the mutual information between the underlying geometric surfaces represented by the point clouds, leading to a regularized CD metric which is robust and computationally efficient for deep learning. We conduct comprehensive experiments for point cloud completion using InfoCD and observe significant improvements consistently over all the popular baseline networks trained with CD-based losses, leading to new state-of-the-art results on several benchmark datasets. Demo code is available at https://github.com/Zhang-VISLab/NeurIPS2023-InfoCD.