You should be able to pull out the metal pin from the connector and carefully pry it apart to remove the old wire, then re-crimp it onto the end of the broken wire. Or if that is a common type of pin you may be able to just crimp on a new pin without trying to save the old one.
Otherwise, I could grab you a used connector with a few inches of wire pigtail so you can cut and splice a new connector in place. There is a 3.0L PRV in an Eagle Premier in one of the junk yards by me that I could grab for you. I think it should be the same connector for the CSV. Can anybody confirm?