Our goal is to introduce CLIMATE-FEVER, a new publicly available dataset for verification of climate change-related claims. By providing a dataset for the research community, we aim to help and encourage work on improving algorithms for retrieving climate-specific information and detecting fake news in social and mass media to reduce the impact of misinformation on the formation of public opinion on climate change. We adapt the methodology of FEVER, the largest dataset of artificially designed claims, to real-life claims collected from the Internet. Although during this process, we could count on the support of renowned climate scientists, it turned out to be no easy task. We discuss the surprising, subtle complexity of modeling real-world climate-related claims within the FEVER framework, which provides a valuable challenge for general natural language understanding. We hope that our work will mark the beginning of an exciting long-term joint effort by the climate science and AI community to develop robust algorithms to verify the facts for climate-related claims.