To cope with growing wireless bandwidth demand, millimeter wave (mmWave) communication has been identified as a promising technology to deliver Gbps throughput. However, due to the susceptibility of mmWave signals to blockage, applications can experience significant performance variability as users move around due to rapid and significant variation in channel conditions. In this context, proactive schedulers that make use of future data rate prediction have potential to bring a significant performance improvement as compared to traditional schedulers. In this work, we explore the possibility of proactive scheduling that uses mobility prediction and some knowledge of the environment to predict future channel conditions. We present both an optimal proactive scheduler, which is based on an integer linear programming formulation and provides an upper bound on proactive scheduling performance, and a greedy heuristic proactive scheduler that is suitable for practical implementation. Extensive simulation results show that proactive scheduling has the potential to increase average user data rate by up to 35% over the classic proportional fair scheduler without any loss of fairness and incurring only a small increase in jitter. The results also show that the efficient proactive heuristic scheduler achieves from 60% to 75% of the performance gains of the optimal proactive scheduler. Finally, the results show that proactive scheduling performance is sensitive to the quality of mobility prediction and, thus, use of state-of-the-art mobility prediction techniques will be necessary to realize its full potential.