We propose an uncoordinated all-to-all broadcast protocol for periodic messages in vehicular networks based on coded slotted ALOHA (CSA). Unlike classical CSA, each user acts as both transmitter and receiver in a half-duplex mode. As in CSA, each user transmits its packet several times. The half-duplex mode gives rise to an interesting design trade-off: the more the user repeats its packet, the higher the probability that this packet is decoded by other users, but the lower the probability for this user to decode packets from others. We compare the proposed protocol with carrier sense multiple access with collision avoidance, currently adopted as a multiple access protocol for vehicular networks. The results show that the proposed protocol greatly increases the number of users in the network that reliably communicate with each other. We also provide analytical tools to predict the performance of the proposed protocol.