Human planning is incredibly efficient. Even in complex situations with many possible courses of action, people are able to make good decisions. Recent proposals suggest that a primary contributor to this efficiency is the intelligent use of cognitive resources, but how people allocate these resources under time constraints is not fully understood. In this work, we conduct a resource-rational analysis of planning in a large data set of online chess games. We first demonstrate that players spent more time thinking when they had more time to do so, and that this effect was especially prevalent when computation was more valuable. Then, we show that additional time spent planning resulted in better selected moves when one existed, and compare between signals of general and immediate time pressure. Finally, we highlight the role of expertise in this setting. Our results provide evidence that people make resource-rational choices when planning under time pressure.