Large cohorts of young adults are poised to add to the working-age population of developing economies. Despite much interest in the consequent growth dividend, the size and circumstances of the potential gains remain under-explored. This study makes progress by focusing on India, which will be the largest individual contributor to the global demographic transition ahead. It exploits the variation in the age structure of the population across Indian states to identify the demographic dividend. The main finding is that there is a large and significant growth impact of both the level and growth rate of the working age ratio. This result is robust to a variety of empirical strategies, including a correction for inter-state migration. The results imply that a substantial fraction of the growth acceleration that India has experienced since the 1980s - sometimes ascribed exclusively to economic reforms - is attributable to changes in the country's age structure. Moreover, the demographic dividend could add about 2 percentage points per annum to India's per capita GDP growth over the next two decades. With the future expansion of the working age ratio concentrated in some of India's poorest states, income convergence may well speed up, a theme likely to recur on the global stage.