To audit the robustness of named entity recognition (NER) models, we propose RockNER, a simple yet effective method to create natural adversarial examples. Specifically, at the entity level, we replace target entities with other entities of the same semantic class in Wikidata; at the context level, we use pre-trained language models (e.g., BERT) to generate word substitutions. Together, the two levels of at- tack produce natural adversarial examples that result in a shifted distribution from the training data on which our target models have been trained. We apply the proposed method to the OntoNotes dataset and create a new benchmark named OntoRock for evaluating the robustness of existing NER models via a systematic evaluation protocol. Our experiments and analysis reveal that even the best model has a significant performance drop, and these models seem to memorize in-domain entity patterns instead of reasoning from the context. Our work also studies the effects of a few simple data augmentation methods to improve the robustness of NER models.