A distributed algorithm is presented for obtaining an efficient and conflict-free broadcasting schedule in a multi-hop packet radio network. The inherent broadcast nature of the radio channel enables a node's transmission to be received by all other nodes within range. Multiple transmissions can be scheduled simultaneously because of the multi-hop nature of the network. It is first shown that the construction of a broadcasting schedule of minimum length is NP-complete, and then a centralized algorithm based on a sequential graph-coloring heuristic is presented to construct minimal-length schedules. A distributed implementation of this algorithm is then proposed, which is based on circulating a token through the nodes in the network.