Legend2TL

The first carbon chassis car was the McLaren MP4/1 which was designed by John Barnard.
McLaren video of Barnard describing the background and history of the MP4/1 which revolutionized racing.
Besides being the first carbon car for McLaren, ever racing and road car built since by McLaren has been a carbon monocoque.

Debuted 35 years ago for the 1981 season, Barnard began working the solution from the end of 1979.
The story about the first accident where the carbon cell saved the driver (John Watson at Monza in 1981) @ 7:00 in the video is amusing as well.
John Barnard, a genius in motorsport engineering

Legend2TL

^ besides being the first F1 car to have a carbon chassis, Barnard also created two other firsts which are still very much in use today in F1

1) 'coke-bottle' tail where the area around the rear of the engine/transmission narrows to allow high pressure air from in front of the rear tires to allow more downforce on the rear diffuser. Debuted in 1983
2) Semi-automatic gearbox, first used on the 1989 Ferrari which also won it's first race with Nigel Mansell at Brazil in 1989.

Not necessarily a household name like Newey/Brawn/Murray/Head, Barnard introduced three critical technologies to F1 that are still in service today.

OK, that's enough of my rambling and droning for a Sunday morning