We define and axiomatically characterize an index of ethnic stratification that measures the extent to which the hierarchy in socio-economic positions across the individuals of a society follows ethnolinguistic lines. This index generalizes the idea of between-group inequality to situations where data on economic and ethnolinguistic distances between pairs of individuals is available. We define an estimator of our index that takes the form of a second order U-statistic and has well-behaved statistical properties, and we show that ethnic stratification is empirically related to low levels of trust in other people and institutions at the local level in Africa.