We introduce a machine learning approach to predict chronic homelessness from de-identified client shelter records drawn from a commonly used Canadian homelessness management information system. Using a 30-day time step, a dataset for 6521 individuals was generated. Our model, HIFIS-RNN-MLP, incorporates both static and dynamic features of a client's history to forecast chronic homelessness 6 months into the client's future. The training method was fine-tuned to achieve a high F1-score, giving a desired balance between high recall and precision. Mean recall and precision across 10-fold cross validation were 0.921 and 0.651 respectively. An interpretability method was applied to explain individual predictions and gain insight into the overall factors contributing to chronic homelessness among the population studied. The model achieves state-of-the-art performance and improved stakeholder trust of what is usually a "black box" neural network model through interpretable AI.