Milanovic, Lindert and Williamson (2007) introduced the concept of the inequality possibility frontier. Their starting point is that very poor societies will never display high Gini indexes of personal distribution of income because there is very little surplus to be appropriated by the upper classes of these societies. The inequality possibility frontier is the maximum level of inequality possible at each level of income. This paper extends the concept to cover regional cases. Countries with populations close to subsistence level inevitably display low regional inequality of income per capita. Rising levels of wealth imply higher attainable degrees of regional inequality. The concepts of regional inequality frontier and regional inequality ratio are presented in this paper, and are illustrated by the case of Brazil between 1872 and 2000.