Immigrants are always accused of stealing people's jobs. Yet, in a neoclassical model of the labor market, there are jobs for everybody and no jobs to steal. (There is no unemployment, so anybody who wants to work can work.) In standard matching models, there is some unemployment, but labor demand is perfectly elastic so new entrants into the labor force are absorbed without affecting jobseekers' prospects. Once again, no jobs are stolen when immigrants arrive. This paper shows that in a matching model with job rationing, in contrast, the entry of immigrants reduces the employment rate of native workers. Moreover, the reduction in employment rate is sharper when the labor market is depressed -- because jobs are more scarce then. Because immigration reduces labor-market tightness, it makes it easier for firms to recruit and improves firm profits. The overall effect of immigration on native welfare depends on the state of the labor market. It is always negative when the labor market is inefficiently slack, but some immigration improves welfare when the labor market is inefficiently tight.