We report the first observation of e(+)e(-) annihilation into states of positive C parity, namely, rho(0)rho(0) and phirho(0). The two states are observed in the pi(+)pi(-)pi(+)pi(-) and K(+)K(-)pi(+)pi(-) final states, respectively, in a data sample of 225 fb(-1) collected by the BABAR experiment at the Positron-Electron Project II e(+)e(-) storage rings at energies near sqrt[s]=10.58 GeV. The distributions of costheta(*), where theta(*) is the center-of-mass polar angle of the phi meson or the forward rho(0) meson, suggest production by two-virtual-photon annihilation. We measure cross sections within the range |costheta(*)|<0.8 of sigma(e(+)e(-)-->rho(0)rho(0))=20.7+/-0.7(stat)+/-2.7(syst) fb and sigma(e(+)e(-)-->phirho(0))=5.7+/-0.5(stat)+/-0.8(syst) fb.