Exclusive ρ+ρ- production in two-photon collisions involving a single highly-virtual photon is studied for the first time with data collected by the L3 experiment at LEP at centre-of-mass energies 89<√s<209GeV with a total integrated luminosity of 854.7 pb−1. The cross section of the process γγ*→ρ+ρ− is determined as a function of the photon virtuality, Q2Q2, and the two-photon centre-of-mass energy, Wγγ, in the kinematic region: 1.2<30GeV2 and 1.1<3GeV. The ρ+ρ−ρ+ρ− production cross section is found to be of the same magnitude as the cross section of the process γγ*→ρ0ρ0, measured in the same kinematic region by L3, and to have similar Wγγ and Q2Q2 dependences