Three-body fragmentation of Na-3(+) ions to Na++Na(3s)+Na(3s) following excitation by He is studied experimentally and theoretically. The three reduced kinetic energies of the products in the center-of-mass are determined for each fragmentation event, and the results are displayed in a Dalitz plot. The fragmentation involves three adiabatic (1)A' electronic states of Na-3(+) that become degenerate at the detector. It is possible to determine the final electronic state for each event, and here we show that each of the three product states appears in a particular sector of the Dalitz plot. Theoretical and experimental Dalitz plots for the three-body fragmentation of Na-3(+) are presented, and the results are related to various mechanisms for three-body fragmentation of this system.