Is there a third US political party?

Yes. Though I suspect you mean at the national level. There are several independents in the United States' Congress who caucus with the major parties. Joe Lieberman is obstensibly an independent (which is similar to being 3rd party but not entirely the same) in the United States' Senate. At the state and local levels, however, 3rd party membership is far more common. Local governments commonly have non-party-affiliated officials, Green Party officials, and some that are even less well known.