  We study the noise-induced escape process in a prototype dissipative
nonequilibrium system, the Ikeda map. In the presence of a chaotic saddle
embedded in the basin of attraction of the metastable state, we find the novel
phenomenon of a strong enhancement of noise-induced escape. This result is
established by employing the theory of quasipotentials. Our finding is of
general validity and should be experimentally observable.
