Do you need a license to fly a balloon?

Yes. A Balloon Pilot Certificate is issued by the Federal Aviation Administration in the USA.

You must pass an FAA written exam, obtain a prescribed number of hours of instruction, make a solo flight, a flight to a specific altitude and pass a flight test.

You don't have to be able to fly an airplane since it is a completely different type of aircraft, although many balloon pilots also fly other types of aircraft like airplanes and helicopters.