Zero-shot stance detection (ZSSD) aims to determine whether the author of a text is in favor of, against, or neutral toward a target that is unseen during training. Despite the growing attention on ZSSD, most recent advances in this task are limited to English and do not pay much attention to other languages such as Chinese. To support ZSSD research, in this paper, we present C-STANCE that, to our knowledge, is the first Chinese dataset for zero-shot stance detection. We introduce two challenging subtasks for ZSSD: target-based ZSSD and domain-based ZSSD. Our dataset includes both noun-phrase targets and claim targets, covering a wide range of domains. We provide a detailed description and analysis of our dataset. To establish results on C-STANCE, we report performance scores using state-of-the-art deep learning models. We publicly release our dataset and code to facilitate future research.