Well, despite being chainsawed through the stomach, then apparently blown up by a grenade, along with the rest of the Sawyer family at the end of Part 2. Leatherface appears to have survived and has moved in with new kinfolk.
Young couple, Ryan (Bill Butler) and Michelle (Kate Hodge), are travelling along the desert highway, when they have a run in with the retarded owner of a gas station. Taking off down a lonely road, which they believe to be a shortcut, they then find themselves being pursued by a lunatic driving a giant 4x4 pickup truck.
They manage to get away from him, but then inadvertently get into an accident with another traveller named Benny (Ken Foree), a survivalist on his way back from a meeting at his training camp. At first he doesn't believe their story about gun toting gas station clerks and chainsaw wielding maniacs driving pick-up trucks, but a sudden appearance by Leatherface (played this time by R A Milhailoff) and his razzing chainsaw makes him change his mind.
With Ryan and Michelle captured and taken back to the family's home, where they are subjected to numerous unpleasantries at the hands of Leatherface's family, which includes a then unknown Viggo Mortensen in an early role. It's down to Benny, armed with his assault rifle, to set out after them and attempt a rescue. But will he reach them in time?
I'm going on the assumption that the folk in this were some sort of relatives of Leatherface, who are now looking after him, but this is never explained, though it doesn't really affect the movie. Directed by Jeff Burr and written by David Schow (didn't he used to have a column in Fangoria mag?) this is by far a much better sequel than Part 2 and is quite enjoyable.
The film was notable for being rejected outright by the UK film censors, when originally submitted for classification back in 1990, but I'm pleased to say in now available here uncut. These days it's notable for being one of Viggo Mortensen's first roles. Good gory fun!