Traffic safety applications using VANET can significantly improve road safety if safety packets can be delivered on time. Therefore, a MAC layer protocol for VANET that can guarantee timely delivery of data is critical. Currently, the MAC layer standard that is supporting inter-vehicular communication is IEEE 802.11 which is a contention based protocol where all the vehicles contend for one common channel. This protocol can not guarantee an upper bounded delay for delivery of safety messages. To resolve this issue, we first obtain the theoretical lower bound on the delay for delivery of safety messages. Then, we introduce a novel MAC layer protocol for inter-vehicular communication that guarantees the delivery of safety messages within a certain upper bound. This upper bound is only within a constant factor from the theoretical lower bound. Our protocol is distributed and dynamic and easily adjusts to the topological changes in the network. Through analytical modeling and simulation, we show that using our MAC layer protocol, the delay in transmission only grows linearly with the number of vehicles even in the dense networks where IEEE 802.11 protocol causes unpredictable delays.