Hi Doug,
Have you tried resolving the EPIC? (using the JIRA workflow)
Deleting is like deleting any other issue. You need to have permissions for 'Delete' in the project. Once you have the permission, click on the epic and choose 'Delete' from the available operations.
If the Epic is something that is worked on, I would take Jared's advise and resolve it instead of deleting it.
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