Revolutionary Cuba since 1959 has outpaced most other Latin American countries at raising life expectancy and reducing infant mortality. Pre-revolutionary Cuba from 1900 to 1959 did even better, however, outperforming all other Latin American countries for which data are available. Pre-revolutionary Cuba became Latin America's unlikely champion of mortality decline despite experiencing slow economic growth and high income inequality, a record that is inconsistent with the “wealthier is healthier” interpretation of mortality reduction. It also achieved this distinction despite being ruled by governments that are sometimes portrayed as corrupt, personalistic, patronage-ridden, subordinate to U.S. business interests, and neglectful, at best, of the exploited and downtrodden. We attribute pre-revolutionary Cuba's rapid mortality decline to its health care system's accessibility to a large fraction of the poor and to features of the island's history, geography, labor union movement, and political system that contributed to this accessibility.