It is widely believed that international cooperation can arise through strategies of reciprocity. In this paper, we investigate whether citizens in the United States and 25 other countries support reciprocity to deal with climate change. We find little public enthusiasm for intrinsic reciprocity, in which countries restrain their consumption of fossil fuels if and only if other countries do the same. In contrast, we find significant support for extrinsic reciprocity, in which countries enforce cooperation by linking issues. Citizens support economic sanctions against polluters and are willing to shame them in international forums, especially when the polluters are violating a treaty. Cooperation could, therefore, emerge from efforts to link climate with other issues and to embed climate commitments in international law.