Vessel trajectory prediction plays a pivotal role in numerous maritime applications and services. While the Automatic Identification System (AIS) offers a rich source of information to address this task, forecasting vessel trajectory using AIS data remains challenging, even for modern machine learning techniques, because of the inherent heterogeneous and multimodal nature of motion data. In this paper, we propose a novel approach to tackle these challenges. We introduce a discrete, high-dimensional representation of AIS data and a new loss function designed to explicitly address heterogeneity and multimodality. The proposed model—referred to as TrAISformer—is a modified transformer network that extracts long-term temporal patterns in AIS vessel trajectories in the proposed enriched space to forecast the positions of vessels several hours ahead.We report experimental results on real, publicly available AIS data. TrAISformer significantly outperforms state-of-the-art methods, with an average prediction performance below 10 nautical miles up to ∼10 hours.