Differences in worker skill cause modest differences in wages within a country, but are associated with massive differences in productivity across countries (Hanushek and Kimko, 2000). I build upon Kremer’s (1993) O-ring theory of production to explain this stylized fact. I posit that there are two kinds of jobs: O-ring jobs where strategic complementarities to skill are large, and a diminishing-returns Foolproof sector, where two mediocre workers provide the same effective labor as one excellent worker. Both production functions are available to each country. In equilibrium, an econometrician would only see small returns to skill within a country. In a world where countries vary only slightly in the average skill of workers, these assumptions are sufficient to generate massive differences in cross-country income inequality while generating only small amounts of intra-country income inequality.