Few problems are as pressing and as existential for the world as climate change, and few have proven to be as intractable. Three decades of international negotiations on climate change have yielded little by way of action that would substantially slow, let alone reverse, human-caused climate change. Can things be different? The answer is yes, but only with an altogether new approach. Cooperation on climate change faces three problems: mutual recrimination between rich and poor countries (the narrative problem), the zero-sum arithmetic of a shrinking global carbon budget (the adding-up problem), and shifts in economic and bargaining power between industrialized and developing countries (the new-world problem). Overcoming them requires radical changes to forge a new Greenprint for cooperation: Large developing countries such as China and India take the lead; All countries focus on technology generation; Industrial countries undertake early emissions cuts while large developing countries make complementary contributions (cuts to energy subsidies, finance for technology development) to strengthen the deal.