We have performed a kinematically complete experiment for triple ionization in atomic collisions. Data were obtained for 3.6-MeV/amu Au53+ impact on Ne. A specific Dalitz representation was developed allowing one to plot in a single spectrum the energy of all three ionized electrons and, simultaneously, obtain information on their emission angles with respect to the projectile direction. The data show distinct fragmentation patterns favoring very asymmetric energy partitionings with one fast and two slow electrons. They are compared to various Classical Trajectory Monte Carlo (CTMC) models. The experimental results are well described only if the electron-electron interaction is included throughout the collision and surprisingly, if the classically modeled electrons are fully correlated in the initial state.