Title: Lossless Data Compression with Transformer. Abstract: Transformers have replaced long-short term memory and other recurrent neural networks variants in sequence modeling. It achieves state-of-the-art performance on a wide range of tasks related to natural language processing, including language modeling, machine translation, and sentence representation. Lossless compression is another problem that can benefit from better sequence models. It is closely related to the problem of online learning of language models. But, despite this ressemblance, it is an area where purely neural network based methods have not yet reached the compression ratio of state-of-the-art algorithms. In this paper, we propose a Transformer based lossless compression method that match the best compression ratio for text. Our approach is purely based on neural networks and does not rely on hand-crafted features as other lossless compression algorithms. We also provide a thorough study of the impact of the different components of the Transformer and its training on the compression ratio.