We report the observation of two-neutrino double-beta decay in Xe-136 with T_1/2 = 2.11 +- 0.04 (stat.) +- 0.21 (sys.) x 10^21 yr. This second order process, predicted by the Standard Model, has been observed for several nuclei but not for Xe-136. The observed decay rate provides new input to matrix element calculations and to the search for the more interesting neutrino-less double-beta decay, the most sensitive probe for the existence of Majorana particles and the measurement of the neutrino mass scale. Show Partial Abstract