Supervised Question Answering systems (QA systems) rely on domain-specific human-labeled data for training. Unsupervised QA systems generate their own question-answer training pairs, typically using secondary knowledge sources to achieve this outcome. Our approach (called PIE-QG) uses Open Information Extraction (OpenIE) to generate synthetic training questions from paraphrased passages and uses the question-answer pairs as training data for a language model for a state-of-the-art QA system based on BERT. Triples in the form of <subject, predicate, object> are extracted from each passage, and questions are formed with subjects (or objects) and predicates while objects (or subjects) are considered as answers. Experimenting on five extractive QA datasets demonstrates that our technique achieves on-par performance with existing state-of-the-art QA systems with the benefit of being trained on an order of magnitude fewer documents and without any recourse to external reference data sources.