Robust data association is necessary for virtually every SLAM system and finding corresponding points is typically a preprocessing step for scan alignment algorithms. Traditionally, handcrafted feature descriptors were used for these problems but recently learned descriptors have been shown to perform more robustly. In this work, we propose a local feature descriptor for 3D LiDAR scans. The descriptor is learned using a Convolutional Neural Network (CNN). Our proposed architecture consists of a Siamese network for learning a feature descriptor and a metric learning network for matching the descriptors. We also present a method for estimating local surface patches and obtaining ground-truth correspondences. In extensive experiments, we compare our learned feature descriptor with existing 3D local descriptors and report highly competitive results for multiple experiments in terms of matching accuracy and computation time. \end{abstract}