We present a factor-proportions trade model in which heterogeneous firms can offshoreintermediate inputs subject to fixed offshoring costs. In the skill-abundant country, high-productivity firms offshore a larger range of labor-intensive inputs to the labor-abundantcountries than low-productivity firms. Differently from the traditional versions of factor-proportions trade theory, Heckscher-Ohlin forces operate at the within-industry level, leadingto endogenous variation in skill intensity across firms that is positively correlated with firmproductivity. Using French firm-level data for the years 1996 to 2007, we provide empirical support for the factor proportions channel through which offshoring to labor-abundantcountries affects the firm-level skill intensities of French manufacturers.