Neural models for automated fact verification have achieved promising results thanks to the availability of large, human-annotated datasets. However, for each new domain that requires fact verification, creating a dataset by manually writing claims and linking them to their supporting evidence is expensive. We develop QACG, a framework for training a robust fact verification model by using automatically generated claims that can be supported, refuted, or unverifiable from evidence from Wikipedia. QACG generates question-answer pairs from the evidence and then converts them into different types of claims. Experiments on the FEVER dataset show that our QACG framework significantly reduces the demand for human-annotated training data. In a zero-shot scenario, QACG improves a RoBERTa model’s F1 from 50% to 77%, equivalent in performance to 2K+ manually-curated examples. Our QACG code is publicly available.