Poor air quality is thought to be an important constraint on human well-being globally, but there exists little direct evidence from the developing world on how health outcomes vary with exposure to polluted air.  We combine household survey-based information on the location and timing of nearly 1 million births across Sub-Saharan Africa with remote sensing based estimates of ambient respirable particulate matter (PM2.5) concentrations to estimate the impact of air quality on African infant mortality. We find that a 10ug/m^3 increase in PM2.5 concentration is associated with a 9% rise in infant mortality across the sample, an effect that has not declined over the last 15 years and which does not diminish at higher household wealth levels.  We estimate that PM2.5 concentrations above minimum exposure levels were responsible for 22% (95% CI: 11-34%) of infant deaths in our 30 study countries and led to 405,000 (203,000-615,000) excess infant deaths in 2015, an estimate more than three times larger than existing attributable death estimates for these countries. Upward revision of disease burden estimates in our African study countries alone would result in a doubling of current estimates of global infant deaths attributable to air pollution.  Even modest reductions in PM2.5 concentrations in our study countries would lead to infant mortality declines larger than the estimated benefits of front-line health interventions, including vaccines and nutritional supplementation.