It is often stated that optimal global climate policy requires a single carbon price throughout the world. Chichilnisky and Heal (1994) argue that distributional issues or lump-sum transfers break this theorem and a policy in which different regions face different carbon prices can become superior to the uniform one. We calculate utilitarian-optimal carbon prices under zero cross-regional lump-sum transfers in the multi-region IAM NICE. The result is optimal global climate policy with different regional carbon prices in which the poorest regions face initially low prices, while the richest regions face very high prices from the outset. This entails significant welfare gains over the standard single price optima commonly reported, which, as we argue briefly in conclusion, can be improved upon still by allowing international trading in the corresponding emissions allocations. Regardless of the parameter values, the welfare gain from considering optimal differential prices is always positive.