Recent advances in antenna and circuit design enable radios that operate in full duplex mode on a single channel with very low residual self-interference. In this paper, the use of such full duplex radios in a wireless local area network (WLAN) is explored. Different scenarios in which the full duplex transmission can be exploited are studied. A distributed full duplex MAC design based on IEEE 802.11 DCF that adopts to the traffic conditions is proposed. The proposed MAC design works for both ad hoc and infrastructure modes of WLAN and takes into consideration new interference and contention during full duplex transmissions. OPNET simulations comparing the performance of the proposed MAC with traditional half duplex based IEEE 802.11 DCF show that the new MAC protocol provides up to 88% throughput gain in a heavily loaded network.