EXO-200 is a single phase liquid xenon detector designed to search for neutrinoless double-beta decay of ^{136}Xe to the ground state of ^{136}Ba. We report here on a search for the two-neutrino double-beta decay of ^{136}Xe to the first 0^+ excited state, 0^+_1, of ^{136}Ba based on a 100 kg\cdotyr exposure of ^{136}Xe. Using a specialized analysis employing a machine learning algorithm, we obtain a 90% CL half-life sensitivity of 1.7 \times 10^{24} yr. We find no statistically significant evidence for the 2\nu\beta\beta decay to the excited state resulting in a lower limit of T^{2\nu}_{1/2} (0^+ \rightarrow 0^+_1) > 6.9 \times 10^{23} yr at 90% CL. This observed limit is consistent with the estimated half-life of 2.5\times10^{25} yr. Show Partial Abstract