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The long queues of unemployed workers at job bureaus and factory gates observed during the Great Depression suggest that jobs are lacking in recessions, irrespec-tive of frictions in matching unemployed workers to recruiting firms. Existing search-and-matching models of unemployment, either with bargained wages as in Pissarides (2000) or with rigid wages as in Hall (2005a), converge asymptotically to full employment when matching frictions disappear, which makes these models inadequate to study recessionary unemployment. In contrast, this paper proposes a search-and-matching model in which jobs are rationed in recessions: the labor mar-ket does not clear at the limit where matching frictions are absent. By constructing a model in which job rationing arises in equilibrium in a frictional labor market, one can begin to understand its macroeconomic implications more rigorously. The distinctive feature of the model is that in recessions, jobs are rationed in the sense that some unemployment remains in the absence of matching frictions. Rationing unemployment measures the shortage of jobs in the absence of match-ing frictions, and frictional unemployment measures additional unemploymen