Intelligent Transportation Systems (ITS) are changing the way cars will drive in the future -- improving, at the same time, the safety and the efficiency of road traffic. Platooning is one of the considered applications, helping cars to drive with very short safety gaps to improve road traffic capacity and to reduce air drag. A fundamental building block for such cooperative driving solutions is reliable and fast wireless communication. Usually, information from the leader of the platoon needs to be broadcast to all members, resulting in large interference ranges, or being relayed from car to car, introducing additional delays. We introduce a Full Duplex Relaying (FDR) system for use in platooning to overcome these limitations. Concentrating on IEEE 802.11p, we implement the system to explore the feasibility and also to conduct a first performance evaluation. Our results clearly demonstrate the significant performance gain, which at the same time allows to further reduce communication overhead and, thus, to safely increase platoon sizes 802.11p, we implement the system to explore the feasibility and also to conduct a first performance evaluation. Our results clearlydemonstrate the significant performance gain, which at the same time allows to further reduce communication overhead and, thus, to safely increase platoon sizes.