Purely character-based language models (LMs) have been lagging in quality on large scale datasets, and current state-of-the-art LMs rely on word tokenization. It has been assumed that injecting the prior knowledge of a tokenizer into the model is essential to achieving competitive results. In this paper, we show that contrary to this conventional wisdom, tokenizer-free LMs with sufficient capacity can achieve competitive performance on a large scale dataset. We train a vanilla transformer network with 40 self-attention layers on the One Billion Word (lm1b) benchmark and achieve a new state of the art for tokenizer-free LMs, pushing these models to be on par with their word-based counterparts.