We argue that a global carbon price is the only way to effectively tackle free riding in international climate policy, required to substantially reduce greenhouse gas emissions. We briefly review the main reasons behind the essential role of carbon pricing, address common misunderstandings and scepticism, and identify key complementary policy instruments. Negotiating global carbon pricing is argued to be much easier than negotiating binding country-level targets, especially if it includes equitable revenue recycling. Moreover, a global carbon price can be more readily adapted to new data and insights of climate science. We propose a political strategy towards a global carbon price that consists of two tracks. The first entails assembly of a carbon-pricing club, a specific case of a climate club, to gradually move towards a full participatory agreement on carbon pricing. The second track involves putting time and energy into re-focusing UNFCCC negotiations on a carbon-pricing agreement. The two tracks reinforce one another, increasing the likelihood of a successful outcome.