ptolemy said:...Mistaken, yes. Read this: http://en.wikipedia.org/wiki/Libya#Libya_under_Gaddafi
By 2004 George W. Bush had lifted the economic sanctions and official relations resumed with the United States. Libya opened a liaison office in Washington, and the United States opened an office in Tripoli. In January 2004, Congressman Tom Lantos led the first official Congressional delegation visit to Libya.[127]
The United States removed Gaddafi's regime, after 27 years, from its list of states sponsoring terrorism.[129]
Perhaps "supporting" was a bit of an overstatement, sorry for the mistake. The US is known for supporting dicators until it doesn't fit their goals anymore (like, you know, Osama Bin Laden and Saddam Husein). They are also historically known for supporting coup d'état when they dont like the democratically chosen governments.