OFDM is an attractive technique to implement multiuser diversity for the downlink. This paper deals with the problem of combining the increased cell throughput of multiuser diversity schemes with a fair distribution of resources among the users. A proportional fair scheduler for opportunistic OFDM is proposed. Its key features are that it can accomodate several quality-of-service (QoS) classes, that it has a tunable fairness level, and that it can be integrated with an opportunistic beamformer to increase system fairness. Simulation results show that the cell throughput of the opportustic scheme approaches that of a more complex smart antenna scheme for many users. For a densely populated system, the proposed scheme shows a graceful QoS degradation, possibly leading to a high average user satisfaction. The fairness parameter effectively tunes the scheduler between high cell throughput and high fairness.