The ability of an autonomous vehicle to perform 3D tracking is essential for safe planing and navigation in cluttered environments. The main challenges for multi-object tracking (MOT) in autonomous driving applications reside in the inherent uncertainties regarding the number of objects, when and where the objects may appear and disappear, and uncertainties regarding objects' states. Random finite set (RFS) based approaches can naturally model these uncertainties accurately and elegantly, and they have been widely used in radar-based tracking applications. In this work, we developed an RFS-based MOT framework for 3D LiDAR data. In partiuclar, we propose a Poisson multi-Bernoulli mixture (PMBM) filter to solve the amodal MOT problem for autonomous driving applications. To the best of our knowledge, this represents a first attempt for employing an RFS-based approach in conjunction with 3D LiDAR data for MOT applications with comprehensive validation using challenging datasets made available by industry leaders. The superior experimental results of our PMBM tracker on public Waymo and Argoverse datasets clearly illustrate that an RFS-based tracker outperforms many state-of-the-art deep learning-based and Kalman filter-based methods, and consequently, these results indicate a great potential for further exploration of RFS-based frameworks for 3D MOT applications.