The multiple ionization of Ar and Xe atoms by fast U 75+ impact has been measured with a projectile-recoil ion time-of-flight technique at 3.6, 5.9, 9.4 and 15.5 MeV/u. Using this technique, the recoil-ion production cross sections can be determined as a function of the final recoil and projectile charge states, i.e. one can distinguish between direct multiple ionization and those processes accompanied by charge transfer. Due to the high projectile charge and high velocity, the direct multiple ionization cross sections to produce highly ionized systems are very large, e.g. the multiple ionization cross section to produce in one collision hydrogen-like Ar exceeds the geometrical Ar-K-shell area. As a consequence of this long range interaction, the kinetic energy of Ar 17+ recoil ions is only of the order of some 10 eV.