This paper endogenizes the market structure of an economy with heterogeneous agents who want to form bilateral matches in the presence of search frictions and when utility is nontransferable. There exist infinitely many marketplaces, and each agent chooses which marketplace to be in: agents get to choose not only whom to match with but also whom they meet with. Perfect segmentation is obtained in equilibrium, where agents match with the first person they meet. All equilibria have the same matching pattern. Although perfect assortative matching is not obtained in equilibrium, the degree of assortativeness is greater than in standard models.