Relative partial ionization cross sections for the formation of Cl-2(+), Cl+ and Cl2+ from molecular chlorine have been recorded as a function of the ionizing electron energy. In these measurements particular attention has been paid to the efficient collection of fragment ions with high translational energies and the minimization of any mass-dependent discrimination effects. The cross sections show that at electron energies above the double ionization threshold the yield of fragment ions can be comparable with the ion yield of nondissociative ionization. Further analysis shows that at electron energies above 50 eV the yield of fragment ions from multiple ionization is comparable with the yield of fragment ions from single ionization: dissociative multiple ionization contributes 14% of the ion yield at 50 eV electron energy and 26% at 100 eV. The decay of Cl-2(2+) by heterolytic cleavage to form Cl2+ is a result of approximately 5% of the dissociative double ionization events. This heterolytic process has a threshold of 41.8 +/- 1.5 eV. Electron-impact induced triple ionization to form long-lived Cl-2(3+) ions has been detected for the first time. This nondissociative triple ionization process makes up approximately 2% of the triple ionization events and triple ionization is responsible for approximately 2% of the ion yield above 100 eV. The threshold for dissociative triple ionization is determined to be 65.3 +/- 1.5 eV, a value in good agreement with a trication precursor state energy derived from the kinetic energy release for the fragmentation of Cl-2(3+) to Cl2+ and Cl+, which provides the first experimental estimate of the triple ionization energy of molecular chlorine.