  Exclusive rho^+ rho^- production in two-photon collisions involving a single
highly-virtual photon is studied with data collected at LEP at centre-of-mass
energies 89 GeV < \sqrt{s} < 209 GeV with a total integrated luminosity of
854.7 pb^-1. The cross section of the process gamma gamma^* -> rho^+ rho^- is
determined as a function of the photon virtuality, Q^2, and the two-photon
centre-of-mass energy, W_gg, in the kinematic region: 1.2 GeV^2 < Q^2 < 30
GeV^2 and 1.1 GeV < W_gg < 3 GeV. The \rho^+\rho^- production cross section is
found to be of the same magnitude as the cross section of the process gamma
gamma^* -> rho^0 rho^0, measured in the same kinematic region by L3, and to
have similar W_gg and Q^2 dependences.
