Isobaric analog states of 7He have been investigated by a novel technique involving the observation of the resonant yield of neutrons from the 6He(p,n) reaction in coincidence with gamma rays from the decay of the (0(+),T=1) state in 6Li. The gamma rays provide a clean signature for the isospin-conserving neutron decay of the low-lying isobaric analog resonances. It is conclusively shown that the analog of the recently observed low-lying spin-orbit partner of the 7He ground state does not exist. Evidence is presented that this state lies at much higher energies, in agreement with microscopic calculations.