It is critical to predict the motion of surrounding vehicles for self-driving planning, especially in a socially compliant and flexible way. However, future prediction is challenging due to the interaction and uncertainty in driving behaviors. We propose planning-informed trajectory prediction (PiP) to tackle the prediction problem in the multi-agent setting. Our approach is differentiated from the traditional manner of prediction, which is only based on historical information and decoupled with planning. By informing the prediction process with the planning of the ego vehicle, our method achieves the state-of-the-art performance of multi-agent forecasting on highway datasets. Moreover, our approach enables a novel pipeline which couples the prediction and planning, by conditioning PiP on multiple candidate trajectories of the ego vehicle, which is highly beneficial for autonomous driving in interactive scenarios.