We study the effects of a dual labor market structure on firm dynamics, the firm size distribution, and aggregate productivity. Using rich Spanish administrative data, we document that the usage of fixed-term (FT) contracts is very heterogeneous across firms within narrowly defined sectors, and that the share of temporary workers increases monotonically with firm size. We write an equilibrium search-and-matching model of firm dynamics with FT and open-ended (OE) contracts to understand the choice of contract type by heterogeneous firms and the equilibrium joint distribution of employment and temporary share across firms. A key feature of the calibrated economy is that matching efficiency is much larger in the FT than in the OE market. Because of this, firms face a trade-off between the lower costs of attracting workers to FT contracts and the higher turnover of FT vacancies. With decreasing returns to scale, the opportunity cost of unfilled vacancies is lower for larger firms, so these firms hire a higher fraction of temporary workers. In equilibrium, the dual labor market structure makes it difficult for firms to become large because of the high turnover of FT contracts and the strong competition of smaller firms for OE contracts. In counterfactual exercises, we find that limiting the duration of FT contracts decreases the share of temporary employment and the unemployment rate, but at the expense of firm destruction and lower aggregate productivity. Instead, making FT contracts more similar to OE contracts by increasing their duration allows the economy to expand through a reduction in the unemployment rate and an increase in aggregate productivity.