The first production Cheyenne III flew for the first time on May 18, 1979, and FAA certification was granted in early 1980.

Compared with the Cheyenne II, the PA-42-720 was about 1 m (3 ft) longer, was powered by 537 kW (720-shp) PT6A-41 turboprops and introduced a T-tail, the most obvious external difference between the PA-31T and PA-42, as well as the most significant change to the series.

[2] In the late 1970s, Piper avoided developing a clean-sheet light business jet to compete with the Cessna Citation I and upgraded its PT6As from 720 to 1,000 hp (540 to 750 kW) Honeywell TPE331-14s.

[3] The aircraft's top speed is 351 kn (650 km/h; 404 mph), faster than the Citation I on most trips while burning one-third less fuel.

It can operate out of 3,000 ft (900 m) runways with a 97 kn (180 km/h) minimum control speed, similar to a King Air 300; it can operate from much shorter hot and high runways than a Citation I and landing distance is shortened by the rotating speedbrake effect of the propellers in beta pitch.