In Chat, if you delete a message, and then paste a permalink to that message, the onebox will show the full content of the "deleted" message. This works for non-moderators (verified on chat.SO).
It's possible to get the message ID of a deleted message by using the web inspector to check its element ID, so you can therefore construct the permalink for any deleted message and view its contents by this message.
As moderators we often remove content when it has personally identifiable information or otherwise must be removed; this circumvents the ability to remove posts. To fully remove a chat post, you would have to edit its content to be empty, then purge its history, then delete it. Once it's been deleted you can't edit it, so any deleted message that wasn't edit-purge-deleted is permanently accessible.