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State-of-the-art neural machine translation methods employ massive amounts of parameters. Drastically reducing computational costs of such methods without affecting performance has been up to this point unsuccessful. To this end, we propose FullyQT: an all-inclusive quantization strategy for the Transformer. To the best of our knowledge, we are the first to show that it is possible to avoid any loss in translation quality with a fully quantized Transformer. Indeed, compared to full-precision, our 8-bit models score greater or equal BLEU on most tasks. Comparing ourselves to all previously proposed methods, we achieve state-of-the-art quantization results.