We study the causes of “nutritional inequality”: why the wealthy eat more healthfully than the poor in the United States. Exploiting supermarket entry, household moves to healthier neighborhoods, and purchasing patterns among households with identical local supply, we reject that neighborhood environments contribute meaningfully to nutritional inequality. Using a structural demand model, we find that exposing low-income households to the same products and prices available to high-income households reduces nutritional inequality by only nine percent, while the remaining 91 percent is driven by differences in demand. These findings counter the common notion that policies to reduce supply inequities, such as “food deserts,” could play an important role in reducing nutritional inequality. By contrast, the structural results predict that means-tested subsidies for healthy food could eliminate nutritional inequality at a fiscal cost of about 15 percent of the annual budget for the U.S. Supplemental Nutrition Assistance Program.