Fairness is an important issue when accessing a shared wireless channel. With fair scheduling, it is possible to allocate bandwidth in proportion to weights of the packet flows sharing the channel. This paper presents a fully distributed algorithm for fair scheduling in a wireless LAN. The algorithm can be implemented without using a centralized coordinator to arbitrate medium access. The proposed protocol is derived from the Distributed Coordination Function in the IEEE 802.11 standard. Simulation results show that the proposed algorithm is able to schedule transmissions such that the bandwidth allocated to different flows is proportional to their weights. An attractive feature of the proposed approach is that it can be implemented with simple modifications to the IEEE 802.11 standard.