Recombination involving the core excitation of two electrons, which may be termed trielectronic recombination, has been experimentally identified for the first time. Using Cl13+ ions circulating in the TSR heavy-ion storage ring, we have observed surprisingly strong low-energy trielectronic recombination resonances, comparable to the dielectronic process. At higher electron-ion collision energies, trielectronic recombination is suppressed due to the autoionization of the triply excited intermediate state into excited final states. The formation of the intermediate state depends sensitively on configuration mixing, making trielectronic recombination a challenge to atomic-structure calculations.