We present limits on Majoron-emitting neutrinoless double-beta decay modes based on an exposure of 112.3 days with 125 kg of Xe-136. In particular, a lower limit on the ordinary (spectral index n = 1) Majoron-emitting decay half-life of Xe-136 is obtained as T_{1/2}^{0\nu\chi^{0}} > 2.6 x 10^{24} yr at 90% C.L., a factor of five more stringent than previous limits. The corresponding upper limit on the effective Majoron-neutrino coupling, using a range of available nuclear matrix calculations, is < (0.8 - 1.6) x 10^{-5}. This excludes a previously unconstrained region of parameter space and strongly limits the possible contribution of ordinary Majoron emission modes to 0\nu\beta\beta decay for neutrino masses in the inverted hierarchy scheme.
