Recent work discovered that training models to be invariant to adversarial perturbations requires substantially larger datasets than those required for standard classification. Perhaps more surprisingly, these larger datasets can be "mostly" unlabeled. Pseudo-labeling, a technique simultaneously pioneered by four separate and simultaneous work in 2019, has been proposed as a competitive alternative to labeled data for training adversarially robust models. However, when the amount of labeled data decreases, the performance of pseudo-labeling catastrophically drops, thus questioning the theoretical insights put forward by Uesato et al. (2019), which suggest that the sample complexity for learning an adversarially robust model from unlabeled data should match the fully supervised case. We introduce Bootstrap Your Own Robust Latents (BYORL), a self-supervised learning technique based on BYOL for training adversarially robust models. Our method enables us to train robust representations without any labels (reconciling practice with theory). This robust representation can be leveraged by a linear classifier to train adversarially robust models. We evaluate BYORL and pseudo-labeling on CIFAR-10 and demonstrate that BYORL achieves significantly higher robustness (i.e., models resulting from BYORL are up to two times more accurate). Experiments on CIFAR-10 against $\ell_2$ and $\ell_\infty$ norm-bounded perturbations demonstrate that BYORL achieves near state-of-the-art robustness with as little as 500 labeled examples. We also note that against $\ell_2$ norm-bounded perturbations of size $\epsilon = 128/255$, BYORL surpasses the known state-of-the-art with an accuracy under attack of 77.61% (against 72.91% for the prior art).