Yes. The explanation is a bit complicated depending on your level of study but it involved radical mechansims (see Wikipedia or similar website). Basically the Cl-Cl bond in chlorine is cleaved creating a Cl radical. This heavy Cl radical bumps into an oxygen molecule in ozone, removing it. Therefore, you are left with oxygen gas and an O radical. But the original Cl radical is not consumed, so the reaction keeps occuring destroying more ozone.