Curly Addams is the deceased great-great-great-great-uncle of Gomez Addams.
He was the brother of Long John Addams, who wrote about their exploits together. He wore a hook on his right arm because his hand was severed by the Governor. The hand, however, lived on, was called Pinky, and is presumably the ancestor of Thing.
The New Addams Family episode:
Curly was played by Michael Roberds.