EXO-200 is a single phase liquid xenon detector designed to search for neutrinoless ββ decay of 136 Xe to the ground state of 136 Ba. We report here on a search for the two-neutrino ββ decay of 136 Xe to the first 0 + excited state, 0 + 1 , of 136 Ba based on a 100 kg·yr exposure of 136 Xe. Using a specialized analysis employing a machine learning algorithm, we obtain a 90% CL half-life sensitivity of 1.7 × 10 24 yr. We find no statistically significant evidence for the 2νββ decay to the excited state resulting in a lower limit of T 2ν 1/2 (0 + → 0 + 1 ) > 6.9 × 10 23 yr at 90% CL. This observed limit is consistent with the estimated half-life of 2.5×10 25 yr.