Evaporation residue cross sections have been measured using neutron-rich radioactive 132Sn beams incident on a 64Ni target in the vicinity of the Coulomb barrier. This is the first experiment using accelerated 132Sn beams to study nuclear reaction mechanisms. The average beam intensity was 2x 104 particles per second and the smallest cross section measured was less than 5 mb. A large sub-barrier fusion enhancement was observed compared to evaporation residue cross sections for 64Ni on stable even Sn isotopes. The enhancement cannot be accounted for by a simple barrier shift due to the change in nuclear sizes. Coupled-channel calculations including inelastic excitation underpredict the measured cross sections below the barrier. The presence of several neutron transfer channels with large positive Q values suggests that multinucleon transfer may play an important role in enhancing the fusion of 132Sn and 64Ni.