The F-4 was my first thought also.
The Phantom II was the first fighter aircraft to be completely reliant on its own radar and detection systems rather than ground based fighter control and was the first fighter to be designed without guns or cannons—being armed with missiles only. However, the elimination of guns proved to be a detriment during close-in air-to-air encounters in Vietnam, which resulted in the installation of guns starting with F-4C.2
http://www.aviation-history.com/mcdonnell/f4.html
One of the big problems with relying on missiles is that sometimes they do not work. Phantom pilots found this out early in the war. The problems with the missiles were eventually fixed but you can’t fix stupid - as in building a fighter plane w/o a gun.