This article studies experimental design in settings where the experimental units are large aggregate entities (e.g., markets), and only one or a small number of units can be exposed to the treatment. In such settings, randomization of the treatment may induce large ex-post estimation biases under many or all possible treatment assignments. We propose a variety of synthetic control designs as experimental designs to select treated units in non-randomized experiments with large aggregate units, as well as the untreated units to be used as a control group. Average potential outcomes are estimated as weighted averages of treated units for potential outcomes with treatment, and control units for potential outcomes without treatment. We analyze the properties of such estimators and propose new inferential techniques.