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Urban plans and infrastructure investments in sub-Saharan Africa need to support human and economic development, while also helping countries and cities stay within the global carbon budget. To date, however, no analyses have focused on the economic costs and benefits of pursuing less carbon-intensive urban growth in sub-Saharan African cities. This is significant as the perception that low-carbon urban development is more expensive than higher-carbon alternatives can be enough to preclude consideration of opportunities for more sustainable development, especially in highly resource-constrained contexts. This paper examines the validity of this perception through an economic appraisal of the scope for low-carbon development in Kigali, Rwanda. We find that the city of Kigali could theoretically invest 0.6% of its GDP each year for 10 years in economically attractive mitigation measures. This would generate annual energy savings equivalent to 1.5% of its GDP and reduce city-scale emissions by 39% by 2032 (relative to business-as-usual trends). The economic case for urban climate action is therefore substantial, and although the city is in some ways unique, this suggests that promising opportunities also exist in other sub-Saharan African cities. However, few national or local governments in the region have the political will and institutional capabilities necessary to realise this mitigation potential. We also find that although potentially significant in the short to medium term, these economically attractive measures would not be sufficient to decouple economic development and greenhouse gas emissions in Kigali in the longer term.