We report the first observation of a double isovector giant dipole state in nuclei (i.e., an isovector giant dipole resonance built on another giant dipole). Two new resonances were observed in (±+,±-) double charge exchange (at T±=292 MeV) on Snat at excitation energies of 24.7 and 28.7 MeV. The energy centroid is very close to the energy at which the double dipole (J±=0+,2+;T=2) state is expected to appear. The angular distributions for the resonances have a clear quadrupole shape. The measured cross sections and the angular distribution agree well with a simple sequential two-step calculation in which single charge exchange through the giant dipole resonance to the double dipole is evaluated.