From 1973 to 2007, private sector union membership in the United States declined from 34 to 8 percent for men and from 16 to 6 percent for women. During this period, inequality in hourly wages increased by over 40 percent. We report a decomposition, relating rising inequality to the union wage distribution's shrinking weight. We argue that unions helped institutionalize norms of equity, reducing the dispersion of nonunion wages in highly unionized regions and industries. Accounting for unions' effect on union and nonunion wages suggests that the decline of organized labor explains a fifth to a third of the growth in inequality--an effect comparable to the growing stratification of wages by education. (Contains 9 figures, 2 tables, and 4 notes.)