The hole in the ozone layer developed mainly due to high emissions of chlorofluorocarbons, or CFCs, which break into radicals in UV light, usually Cl radicals, which then react with ozone like so (' represents a radical):
Cl'(g) + O3(g) --> O2(g) + ClO'(g)
ClO'(g)+ 2O3(g) --> 2O2(g) + Cl'(g)
As you can see, one chlorine radical can theoretically break down an infinite amount of ozone, which is why it is so destructive. The only way to stop the reaction is if two radicals meet, and form a stable compound.