Excitonic solar cells, comprised of materials such as organic semiconductors, inorganic colloidal quantum dots, and carbon nanotubes, are fundamentally different than crystalline, inorganic solar cells in that photogeneration of free charge occurs through intermediate, bound exciton states. Here, we show that the Second Law of Thermodynamics limits the maximum efficiency of excitonic solar cells below the maximum of 31% established by Shockley and Queisser [J. Appl. Phys. 32, 510 (1961)] for inorganic solar cells (whose exciton-binding energy is small). In the case of ideal heterojunction excitonic cells, the free energy for charge transfer at the interface, \ensuremath{\Delta}$G$, places an additional constraint on the limiting efficiency due to a fundamental increase in the recombination rate, with typical \ensuremath{-}\ensuremath{\Delta}$G$ in the range 0.3 to 0.5 eV decreasing the maximum efficiency to 27% and 22%, respectively.