We study a parsimonious model of a competitive labor market in which firms privately screen workers to identify talent. The equilibrium exhibits dispersion in wages and productivity; when talent is scarce, firms with superior screening skills post higher wages, attract better applicants, and recruit more talented workers. High-wage firms impose a compositional externality on low-wage firms, leading to equilibrium inefficiency: Welfare would be higher if low-skilled firms posted high wages and selected first. We also provide a micro-foundation for firms heterogeneous screening skills. When talented workers are better at screening (e.g. via superior referrals), a dynamic version of the economy converges to a unique steady state in which differences in talent, profits and screening skills persist forever.