The original Plymouth Barracuda was built upon the A-body chassis, which was also common to several other vehicles manufactured by Chrysler, including the popular Dodge Dart. The 1964 model was offered as an option of the Valiant line and carried Valiant insignia. It was designed to appeal to a sportier market, and some might claim it was the first pony car because it preceded the Ford Mustang to market by two weeks. However, the Mustang, unlike the Barracuda, featured a completely unique body style from the car on which it was based (the Ford Falcon), making it the first true pony car. Plymouth's executives initially wanted to call the car the 'Panda' but the designers complained and John Samsen's idea of 'Barracuda' was chosen.
The first generation Barracuda's distinctive feature was its enormous fastback wrap-around rear window, considered the largest piece of automotive glass ever installed at that time (14.4 square feet). Power trains were identical to the Valiant's, including two versions of Chrysler's legendary inline "slant 6" — a 170 in³ (2.8 L), 101 hp (75 kW) version and an optional 225 in³ (3.7 L), 145 hp (108 kW) version offered. A two-barrel carbureted 180 hp (134 kW) 273 in³ (4.5 L) V8 was the top engine option for 1964, so performance at first was modest. The 170 in³ six was later eliminated leaving the 225 in³ 145 hp version as the smallest engine option. The Barracuda sold for a base price of US$2,512, and unlike any other year, all 1964 Barracudas with automatic transmissions had push button shifters on their dashboards.
The 1965 model year saw the introduction of two important options; the 273 in³ (4.5 L) Commando, a 235 hp (175 kW) four-barrel carbureted V8, and the Formula 'S' package, a performance package that included the Commando V8, upgraded suspension, wheels, and tires, and a standard tachometer.
In 1966 the Barracuda would receive a new taillight design and a facelift, making it easily distinguishable from the 1964 and 1965 versions. As a move to further the car's image from that of the Valiant, the blue and red "V" shaped Valiant emblem below the rear glass on the center of the vehicle was replaced mid-year by a Barracuda fish emblem. The 1966 model had updated sheet metal, which gave a more chiseled contour to the fenders, and also featured fender-top turn signal indicators in the shape of shark fins. Also new were full-sized bumpers and a unique "cheese-grater" grill, which slanted forward aggressively and featured a distinct grid pattern. Other changes for 1966 included a redesigned gauge cluster and optional center console.
Since 1967 saw a complete redesign of the Barracuda, some collectors consider the 1966 model a unique, one-year-only rarity. Other early A-body enthusiasts shun the 1966 version as an unfortunate departure from the original design.