Abstract: The ability to precisely control the movement of excitations can aid in the design of excitonic circuits, with potential applications in bioimaging, microscopic signaling, or new forms of solar energy capture. Here, we demonstrate theoretically that an organic single-molecule exciton "transistor," or exciton gate, can be designed through the careful use of second excited singlet states (S2 states). This design makes it possible to control the direction and distance that an exciton travels, by using either an external light source or an auxiliary exciton source for control. We demonstrate how to overcome the two main obstacles for the strategy to be viable. First, molecules with long-lived S2 states must be used, which limits the design to a small subset of possible molecules. Second, exquisite control of the relative orientations of molecules is required to properly align transition dipole moments, necessitating the use of a nanodesign method such as DNA origami. We introduce a rate model that relates decay rates and orientational errors to the probability that the exciton gate produces false positives and false negatives. Finally, in analogy to traditional transistors, we show how a universal set of logical binary gates may be constructed with these exciton gates, demonstrating that universal computation becomes possible.