The differential cross section for electron-induced neutron knockout in the reaction 4He(e,e(')n)(3)He has been measured for the first time with a statistical accuracy of 11%. The experiment was performed in quasielastic kinematics at a momentum transfer of 300 MeV/c and in the missing-momentum range of 25-70 MeV/c. The comparison of the data with theoretical calculations shows an impressive increase of the cross section resulting from final state interaction effects. Specifically, the p-n charge-exchange process dominates the cross section in this kinematical regime.