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, Q2, and the two-photon centre-of-mass energy, Wγγ, in the kinematic region: 1.2