We study the causes of “nutritional inequality”: why the wealthy eat more healthfully than the poor in the United States. Exploiting supermarket entry and household moves to healthier neighborhoods, we reject that neighborhood environments contribute meaningfully to nutritional inequality. We then estimate a structural model of grocery demand, using a new instrument exploiting the combination of grocery retail chains’ differing presence across geographic markets with their differing comparative advantages across product groups. Counterfactual simulations show that exposing low-income households to the same products and prices available to high-income households reduces nutritional inequality by only about 10%, while the remaining 90% is driven by differences in demand. These findings counter the argument that policies to increase the supply of healthy groceries could play an important role in reducing nutritional inequality.