The widely varied meanings of the term “social structure” rob it of usefulness. Following Durkheim, social structure should refer to extra-individual, positively ascertainable social facts that exert constraint on individuals. We examine the impact of inequality on association, specifically on marriage within and among social strata. The constraint that inequality exerts on intermarriage is less obvious than the notion that inequality increases the motive for status homogamy. A mathematical model, derived in the Appendix, indicates, however, that inequality constrains people to marry unequals. Data for 125 SMSAs for intermarriage with respect to education, socioeconomic index, and income show that the model works well for education and socioeconomic index. The paradox of structure and constraint is that greater structural inequality is imported into the pair relations among population members in the face of empirically evident aversion to relations bridging status distance. Inequality is antagonistic to homogamy.