Users often fail to formulate their complex information needs in a single query. As a consequence, they may need to scan multiple result pages or reformulate their queries, which may be a frustrating experience. Alternatively, systems can improve user satisfaction by proactively asking questions of the users to clarify their information needs. Asking clarifying questions is especially important in conversational systems since they can only return a limited number of (often only one) result(s). In this paper, we formulate the task of asking clarifying questions in open-domain information-seeking conversational systems. To this end, we propose an offline evaluation methodology for the task and collect a dataset, called Qulac, through crowdsourcing. Our dataset is built on top of 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 170% retrieval performance improvement in terms of P@1, which clearly demonstrates the potential impact of the task. We further propose a retrieval framework consisting of three components: question retrieval, question selection, and document retrieval. In particular, our question selection model takes into account the original query and previous question-answer interactions while selecting the next question. Our model significantly outperforms competitive baselines. To foster research in this area, we have made Qulac publicly available.