In multihop wireless ad hoc networks, interference from transmissions on nearby links makes it difficult to predict available bandwidth and reserve bandwidth for Constant Bit Rate traffic. In this paper, we present a MAC layer scheme that supports constant bit rate traffic through transmission scheduling. The paper details the sufficient condition on bandwidth requirement, and presents a time slot assignment algorithm that assigns each link a number of slots proportional to the traffic load on itself. The theoretical analysis proves that the sufficient condition is indeed sufficient to provide a network-wide collision-free transmission schedule, and the time slot assignment algorithm can completely avoid the hidden and exposed terminal problems. Through extensive simulations, we verified that a TDMA scheme serves much better than a random, contention-based scheme in the context of maximizing network throughput and providing guaranteed end-to-end data rate.