Accurate estimation of air quality impacts on health outcomes is critical for guiding policy choices to mitigate such damages. Estimation poses an empirical challenge, however, because local economic activity can simultaneously generate changes in both air quality and in health impacts that are independent of air quality, confounding pollution-health estimates. To address this challenge, we leverage plausibly exogenous variation in local particulate matter exposure across sub-Saharan Africa due to dust export from the Bodele Depression, a remote Saharan region responsible for a substantial share of global atmospheric dust. Large scale transport of this dust is uncorrelated with local emissions sources and allows us to isolate the causal impact of air quality on infant mortality across sub-Saharan Africa. Combining detailed information on nearly 1 million births with satellite measures of aerosol particulate matter, we find that a 10mg/m3 increase in local ambient PM2.5 concentration driven by distant dust emission causes a 22% increase in infant mortality across our African sample (95% CI: 10-35%), an effect comparable to quasi-experimental pollution-infant mortality estimates from wealthier countries. We also show that rainfall over the Bodele is a significant control on PM2.5 export and thus child health, and that future climate-change driven changes in Saharan rainfall could generate very large impacts on African child health through this pathway alone. We calculate that seemingly exotic proposals to pump and apply groundwater to the Bodele to reduce dust emission could be cost competitive with leading interventions aimed at improving child health.