This paper estimates the redistributive effects of welfare state expenditures on children and disparities in the economic well-being of children in ten nations and relates the two. Data from the Organization for Economic Cooperation and Development (OECD) and other sources for cash and non-cash social welfare benefits are used to describe differences in the size and nature of welfare states and their distributional effects. The OECD data are combined with micro data on household incomes from the Luxembourg Income Study (LIS) both to estimate the redistributive effects of the expenditures and taxes and to construct measures of the differences in the relative standard of living among children at various points in the income distributions of their countries. These measures may be thought of as capturing at least one of the essentials of the degree to which the poorest children in the country have a 'fair chance' and 'an equal opportunity chance' to succeed economically. The results indicate a wide range of differences in levels of economic resources and support for children within, as well as between, nations. The degree to which children have fair and equal opportunity chances varies considerably across countries and depends critically upon welfare state benefits. Taking account of non-cash benefits substantially reduces cross national differences, but does not eliminate them. Subject to a number of qualifications mentioned at the end of the paper, we find that non-cash benefits are particularly important for low-income American children and their families.