This paper presents a medium access control protocol for wireless networks that improves system spectral efficiency using multiple channels. Use of multiple narrow channels has already been proposed as a solution to reduce MAC overhead, but merely dividing a wide channel into narrow channels cannot mitigate the negative effect of packet collisions especially when the network is densely populated. The proposed protocol, called N-DCF, adds protocol support to reduce packet collisions and improve channel utilization. The main idea is to let each node contend on one of the multiple channels and give the node privilege to access other channels when it successfully finishes transmission on its contention channel. When a node gains privilege to a channel, it can access the channel without contention. Privilege is gained probabilistically so that other nodes can have chance to win the channel and obtain privilege for other channels as well. N-DCF reduces channel idle time by conducting random backoff only on one of the narrow channels and reduces packet collisions by assigning contention channel randomly. Idle channels are not wasted because nodes can access other channels once the node wins its contention channel. Performance evaluation shows that the proposed scheme achieves higher throughput than 802.11 DCF without harming the fairness, regardless of node density, packet size, and number of radios.