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Chest Computational Tomography (CT) scans present low cost, speed and objectivity for COVID-19 diagnosis and deep learning methods have shown great promise in assisting the analysis and interpretation of these images. Most hospitals or countries can train their own models using in-house data, however empirical evidence shows that those models perform poorly when tested on new unseen cases, surfacing the need for coordinated global collaboration. Due to privacy regulations, medical data sharing between hospitals and nations is extremely difficult. We propose a GAN-augmented federated learning model, dubbed ST-FL (Style Transfer Federated Learning), for COVID-19 image segmentation. Federated learning (FL) permits a centralised model to be learned in a secure manner from heterogeneous datasets located in disparate private data silos. We demonstrate that the widely varying data quality on FL client nodes leads to a sub-optimal centralised FL model for COVID-19 chest CT image segmentation. ST-FL is a novel FL framework that is robust in the face of highly variable data quality at client nodes. The robustness is achieved by a denoising CycleGAN model at each client of the federation that maps arbitrary quality images into the same target quality, counteracting the severe data variability evident in real-world FL use-cases. Each client is provided with the target style, which is the same for all clients, and trains their own denoiser. Our qualitative and quantitative results suggest that this FL model performs comparably to, and in some cases better than, a model that has centralised access to all the training data.