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We propose a medium access control (MAC) protocol for an ad hoc network of mobile wireless terminals that are equipped with multiple directional antennas. Use of directional antennas in ad hoc networks can largely reduce the radio interference, thereby improving the packet throughput. However, the main problem of using directional antennas in such networks is due to the dynamic nature of the network caused by frequent node movements. This gives rise to problems such as locating and tracking during random channel access. The MAC protocol presented in this paper proposes a solution to these problems without the help of additional hardware. Results obtained from detailed computer simulations demonstrate the performance improvement obtained with the proposed scheme.