This paper studies the assignment of heterogeneous workers to heterogeneous jobs. Owing to the anonymity of a large labor market, workers use mixed strategies when applying for jobs. This randomness generates coordination frictions. Two workers may apply for a particular job, whereas an identical job gets no applications. The model generates assortative matching, with a positive but imperfect correlation between matched workers’ and firms’ types. It predicts that a worker’s wage is increasing in her job’s productivity and a firm’s profit is increasing in its employees’ productivity. The model also yields a version of the welfare theorems.