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Building a question-answering agent currently requires large annotated datasets, which are prohibitively expensive. This paper proposes Schema2QA, an open-source toolkit that can generate a Q&A system from a database schema augmented with a few annotations for each field. The key concept is to cover the space of possible compound queries on the database with a large number of in-domain questions synthesized with the help of a corpus of generic query templates. The synthesized data and a small paraphrase set are used to train a novel neural network based on the BERT pretrained model. We use Schema2QA to generate Q&A systems for five Schema.org domains, restaurants, people, movies, books and music, and obtain an overall accuracy between 64% and 75% on crowdsourced questions for these domains. Once annotations and paraphrases are obtained for a Schema.org schema, no additional manual effort is needed to create a Q&A agent for any website that uses the same schema. Furthermore, we demonstrate that learning can be transferred from the restaurant to the hotel domain, obtaining a 64% accuracy on crowdsourced questions with no manual effort. Schema2QA achieves an accuracy of 60% on popular restaurant questions that can be answered using Schema.org. Its performance is comparable to Google Assistant, 7% lower than Siri, and 15% higher than Alexa. It outperforms all these assistants by at least 18% on more complex, long-tail questions.