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Prior studies of zero-shot stance detection identify the attitude of texts towards unseen topics occurring in the same document corpus. Such task formulation has three limitations: (i) Single domain/dataset. A system is optimized on a particular dataset from a single domain; therefore, the resulting system cannot work well on other datasets; (ii) the model is evaluated on a limited number of unseen topics; (iii) it is assumed that part of the topics has rich annotations, which might be impossible in real-world applications. These drawbacks will lead to an impractical stance detection system that fails to generalize to open domains and open-form topics. This work defines OpenStance: open-domain zero-shot stance detection, aiming to handle stance detection in an open world with neither domain constraints nor topic-specific annotations. The key challenge of OpenStance lies in the open-domain generalization: learning a system with fully unspecific supervision but capable of generalizing to any dataset. To solve OpenStance, we propose to combine indirect supervision, from textual entailment datasets, and weak supervision, from data generated automatically by pre-trained Language Models. Our single system, without any topic-specific supervision, outperforms the supervised method on three popular datasets. To our knowledge, this is the first work that studies stance detection under the open-domain zero-shot setting. All data and code are publicly released.