This paper studies the labor market impact of documented and undocumented immigration in a model with search frictions and non-random hiring. Since immigrants accept lower wages, firms obtain a higher match surplus from hiring immigrants rather than natives. Therefore, immigration results in the creation of additional jobs but also generates more job competition. Whether job creation or competition is the dominating effect depends on the size of the induced fall in expected wages paid by firms. Using US data, I show in my empirical analysis that among low-skilled workers undocumented immigrants earn 8% less and have a 7 ppt higher job finding rate than documented immigrants. Parameterizing the model based on these estimates, I find that the job creation effect of undocumented immigration dominates the job competition effect and leads to gains in terms of both employment and wages for native workers. In contrast, documented immigration leads to a fall in natives' employment due to its weaker job creation effect. A policy of stricter immigration enforcement, simulated by a rise in the deportation rate of undocumented workers, decreases firms' expected match surplus, mutes job creation and thus raises the unemployment rates of all workers.