We address the problem of improving the throughput and delay efficiency of distributed multi-channel MAC (MMAC) protocols. We design an MMAC protocol called FD-MMAC that exploits recent advances in full-duplex (FD) communications to coordinate channel access in a distributed manner. Compared with prior MMAC designs, the FD-MMAC protocol eliminates the use of in-band or out-of-band control channels for combating the multi-channel hidden terminal problem, discovering the resident channel of destinations, and performing load balancing. Furthermore, FD-MMAC improves the spectral efficiency by enabling the operation of multi-channel exposed terminals. To achieve its goals, FD-MMAC integrates an advanced suite of PHY-layer techniques, including self interference suppression, error vector magnitude and received power measurements, and signal correlation techniques. We validate the proposed PHY-layer techniques on NI USRP devices. Further, we show via simulations that FD-MMAC achieves significantly higher throughput and lower delay compared with prior art.