I am actually going to take the answer to this from one of my favorite organizations 'The Union of Concerned Scientists'. This comes directly from their website under frequently asked questions about global warming:

This site has a lot of interesting and reliable answers to questions about global warming, so please refer to it in for more detail on this topic.

Is global warming connected to the hole in the ozone layer?

Global warming and ozone depletion are two separate but related threats. Global warming and the greenhouse effect refer to the warming of the lower part of the atmosphere (also known as the troposphere) due to increasing concentrations of heat-trapping gases. By contras, the ozone hole refers to the loss of ozone in the upper part of the atmosphere, called the stratosphere. This is of serious concern because stratospheric ozone blocks incoming ultraviolet radiation from the sun, some of which is harmful to plants, animals, and humans.

The two problems are related in a number of ways, including:

* Some human-made gases, called chlorofluorocarbons, trap heat and destroy the ozone layer. Currently, these gases are responsible for less than 10 percent of total atmospheric warming, far less than the contribution from the main greenhouse gas, carbon dioxide.

* The ozone layer traps heat, so if it gets destroyed, the upper atmosphere actually cools, thereby offsetting part of the warming effect of other heat-trapping gases. But that's no reason to rejoice: the cooling of the upper layers of the atmosphere can produce changes in the climate that affect weather patterns in the higher latitudes.

* Trapping heat in the lower part of the atmosphere allows less heat to escape into space and leads to cooling of the upper part of the atmosphere. The colder it gets, the greater the destruction of the protective ozone layer.

Reducing ozone-depleting gases is crucial to preventing further destruction of the ozone layer, but eliminating these gases alone will not solve the global warming problem. On the other hand, efforts to reduce all types of emissions to limit global warming will also be good for the recovery of the ozone layer.