Comparing two countries in which the poor have equal real incomes, the one in which the rich are wealthier is likely to have a higher infant mortality rate. This anomalous result does not appear to spring from measurement error in estimating the income of the poor, and the association between high infant mortality and income inequality is still present after controlling for other factors such as education, medical personnel, and fertility. The positive association of infant mortality and the income of the rich suggests that measured real incomes may be a poor measure of social welfare.