Adversarial attacks against deep neural networks (DNNs) are continuously evolving, requiring increasingly powerful defense strategies. We develop a novel adversarial defense framework inspired by the adaptive immune system: the Robust Adversarial Immune-inspired Learning System (RAILS). Initializing a population of exemplars that is balanced across classes, RAILS starts from a uniform label distribution that encourages diversity and debiases a potentially corrupted initial condition. RAILS implements an evolutionary optimization process to adjust the label distribution and achieve specificity towards ground truth. RAILS displays a tradeoff between robustness (diversity) and accuracy (specificity), providing a new immune-inspired perspective on adversarial learning. We empirically validate the benefits of RAILS through several adversarial image classification experiments on MNIST, SVHN, and CIFAR-10 datasets. For the PGD attack, RAILS is found to improve the robustness over existing methods by >= 5.62%, 12.5% and 10.32%, respectively, without appreciable loss of standard accuracy.