The fastest way to do this is by adding your Production org in Force.com IDE / Eclipse and delete the class via the IDE. You will have to make sure that no dependencies exist before deleting, else the delete will fail.
Remove the dependencies by deleting the class first in your sandbox, then seeing why the delete would fail, do those changes, deploy it to your production org, then delete the class via Eclipse
Edit: You could also use the Force.com Migration Tool with Apache Ant to make desctructive changes, however this takes a little coding and installing ant and generally takes a little longer to set up compared to the eclipse method if you only need to do this a few times. more about that here: http://wiki.developerforce.com/page/Propagating_Destructive_Changes