Recent experimental results have provided unambiguous evidence that neutrinos have a small but finite mass and mix from one type into another. The phenomenon of neutrino mixing is characterized by the coupling between the neutrino flavor (nu_{e,mu,tau}) and mass eigenstates (nu_{1,2,3}) and the associated mixing angles. Previous neutrino oscillation experiments have determined two of the three mixing angles in the neutrino mixing matrix, U_{MNSP}. Using multiple neutrino detectors placed at different distances from a nuclear power plant, a future reactor neutrino experiment has the potential to discover and measure the coupling of the electron neutrino flavor to the third mass eigenstate, U_{e3}, the last undetermined element of the neutrino mixing matrix.