It is widely believed that the implicit regularization of stochastic gradient descent (SGD) is fundamental to the impressive generalization behavior we observe in neural networks. In this work, we demonstrate that non-stochastic full-batch training can achieve strong performance on CIFAR-10 that is on-par with SGD, using modern architectures in settings with and without data augmentation. To this end, we utilize modified hyperparameters and show that the implicit regularization of SGD can be completely replaced with explicit regularization. This strongly suggests that theories that rely heavily on properties of stochastic sampling to explain generalization are incomplete, as strong generalization behavior is still observed in the absence of stochastic sampling. Fundamentally, deep learning can succeed without stochasticity. Our observations further indicate that the perceived difficulty of full-batch training is largely the result of its optimization properties and the disproportionate time and effort spent by the ML community tuning optimizers and hyperparameters for small-batch training.