We report the first observation of the isospin splitting of the giant dipole resonance built on the isobaric analog state. Three giant resonances were observed in (+,-) double charge exchange (at T=292 MeV) on Fe56 at excitation energies of 25.7, 30.0, and 33.5 MeV (Q=-31.4, -35.7, and -39.2 MeV). Angular distributions were measured for the resonances and each observed to have a dipole shape. The cross-section ratios of the resonances are in close agreement with simple isospin geometry arguments for an isovector excitation built on the isobaric analog state. The summed cross section agrees well with simple sequential-model calculations in which the intermediate states arise from single charge exchange to the isobaric analog state and to the giant dipole resonance. We identify the three resonances as the isospin members of the charge-exchange dipole built on the isobaric analog state.