Hunter is suing former Edwards aide John Young and his wife for the video and some still images.
Hunter claims the material is her property, but the Youngs have argued that Hunter lost rights to it because she left it behind at a house in Chatham County where they lived with Hunter for a time.
The existence of the tape came to light after Young's book "The Politician," hit the stands in February. In the book, Young documents his years working for Edwards and talks about his role hiding the existence of Edwards' affair with Hunter from the media while he ran for president.
Edwards has publicly admitted to fathering a child with Hunter.
The judge overseeing the lawsuit currently has the disputed video under lock and key. Superior Court Judge Allen Baddour has also ordered Hunter's deposition be sealed for 45 days. After that, he told both sides he will consider arguments for keeping all or part of Hunter's testimony secret for a longer period.
Young's attorneys have challenged the need for secrecy, pointing out that Hunter has given in depth interviews to Oprah Winfrey and GQ Magazine about her affair with Edwards and the daughter it produced.