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Users often fail to formulate their complex information needs in a single query. As a consequence, they need to scan multiple result pages and/or reformulate their queries, which is a frustrating experience. Alternatively, systems can improve user satisfaction by proactively asking questions from the users to clarify their information needs. Asking clarifying questions is especially important in information-seeking conversational systems, since they can only return a limited number (often only one) of results. In this paper, we formulate the task of asking clarifying questions in open-domain information retrieval. We propose an offline evaluation methodology for the task. In this research, we create a dataset, called Qulac, through crowdsourcing. Our dataset is based on the TREC Web Track 2009-2012 data and consists of over 10K question-answer pairs for 198 TREC topics with 762 facets. Our experiments on an oracle model demonstrate that asking only one good question leads to over 100% retrieval performance improvement, which clearly demonstrates the potential impact of the task. We further propose a neural model for selecting clarifying question based on the original query and the previous question-answer interactions. Our model significantly outperforms competitive baselines. To foster research in this area, we have made Qulac publicly available.