In federated learning, fair prediction across various protected groups (e.g., gender, race) is an important constraint for many applications. Unfortunately, prior work studying group fair federated learning lacks formal convergence or fairness guarantees. Our work provides a new definition for group fairness in federated learning based on the notion of Bounded Group Loss (BGL), which can be easily applied to common federated learning objectives. Based on our definition, we propose a scalable algorithm that optimizes the empirical risk and global fairness constraints, which we evaluate across a number of common fairness and federated learning benchmarks. Our resulting method and analysis are the first we are aware of to provide formal theoretical guarantees for training a fair federated learning model.