The film opens on the date of August 18, 1973 by revealing that a cemetery in rural Texas has been vandalized; several gravesites have been desecrated, the bodies dug up and arranged into bizarre "sculptures". Sally Hardesty (Marilyn Burns) and her invalid, wheelchair-bound brother, Franklin (Paul A. Partain), are concerned that their grandfather's grave may have been vandalized, so they travel to the site with three of their friends, Sally's boyfriend Jerry (Allen Danziger), her best friend Pam (Teri McMinn), and Pam's boyfriend Kirk (William Vail). When they discover that the grave is intact, they decide to visit the old family homestead which is now abandoned.
Along the way, they pass a slaughterhouse and Franklin describes how cattle used to be killed with a sledgehammer, and now they use an air gun. Shortly afterwards, they pick up a skinny, strange-looking hitch hiker (Edwin Neal) who exhibits bizarre behavior. After inviting the group back to his house for dinner, an invitation they all decline, the hitchhiker takes a photo of Franklin with an instant polarid camara, and demands a two-dollar payment for it. When Franklin refuses, the man angrily crumples the photo, sets it on fire, and cuts his own hand with Franklin's pocket knife. The guys manage to throw him out of the van, but not before he cuts Franklin with the knife, too. Before they can drive away, he smears blood on their van.
Running low on fuel, they stop at a rural Gulf filling station, only to have the strange-looking old man who runs it (Jim Siedow) tell them that the tanks are empty and that he's waiting for the gas tanker to show up. When the old man learns that their destination is the old Hardesty home, he advises the young people against going there by saying that the people who live around that area are not receptive to strangers. They buy some barbeque sandwiches from the old man and depart for the family home which they finaly arrive a short while later.
While Sally and Pam go off to look through the abandoned house, Franklin finds it hard to get around the old place due to his wheelchair, and he is frustrated by the fun that the two couples seem to be having.
Franklin gives Pam and Kirk directions to an old swimming hole that used to be nearby, but they find it completely dried up. Kirk hears the sound of a gas generator nearby and gets the idea to find out where it is and barter for some gasoline. Following the sound, they discover a large farm house surrounded by numerous abandonded vehicles, partially hidden by a large tarp. Kirk finds a human tooth on the front porch and frightens Pam with it. He gets no answer to a knock at the door, and he is lured inside by strange animal sounds. He goes into the house and in the space of a few moments, an enormous heavyset man in a weird mask (Gunnar Hansen) appears and murders him with a blow to the head via sledgehammer. The man, known as "Leatherface" due to his mask made out of a human face, drags the body into a back room.
Pam becomes restless when Kirk does not return, and she goes into the house to look for him. She stumbles into a room that is filled with human and animal bones. A live chicken dangles in a small bird cage. Weird sculptures made out of human skulls hang from the ceiling. Furniture is adorned with human bones and skulls. The floor is covered with bits of bones and feathers. Pam begins to retch and starts screaming, when Leatherface appears and lunges for her. She runs out onto the porch but he catches her, carrying her kicking and screaming back into the house, where he savagely hangs her on a meat hook through her back. While she hangs there, she can see Leatherface dismembering the dead body of Kirk with a chainsaw.
Back at the Hardesty house, Sally and the others start to wonder why Pam and Kirk have not returned. As the sun begins to set, Jerry sets out in the general direction and also comes upon the house after he is lured to the area by the sound of the house's gas generator. He is alerted by the blanket that Kirk left hanging on the front porch, and he goes into the house. After Jerry walks into the kitchen, he discovers Pam locked inside a large freezer, still alive but convulsing and near death. She lunges out of the freezer just as Leatherface appears and kills Jerry with the sledgehammer. He forces Pam's body back into the freezer and locks it again. Leatherface is clearly distraught, apparently upset because strangers keep coming to his house.
At nightfall, Sally and Franklin are forced to go after Jerry when he does not return; Jerry took the keys to the van with him when he left. Franklin refuses to wait at the van and insists that Sally push his wheelchair along the unpaved path through the woods. Before they get to the house, they are attacked by Leatherface, who murders Franklin by ramming him in the chest with a chainsaw. Sally flees in terror with Leatherface directly behind her. She gets cut on the thorny brush as she runs, eventually reaching the house; she is unaware that the house belongs to her pursuer. Sally runs upstairs as Leatherface saws through the front door to get at her. In an upstairs bedroom, she finds two dessicated figures, an old man and old woman. The woman is long dead, but the old man is still barely alive, hideously withered. Leatherface corners her on the second floor, so she leaps out a window and runs from the house again with him right behind her.
Sally reaches the gas station and Leatherface disappears. The old man says he's going to take Sally to get help, and while he's gone Sally notices the smoke pit where the barbeque is made. She stares at it in fascination. The old man returns and suddenly attacks Sally, who tries to defend herself with a kitchen knife. But the old man knocks the knife out of Sally's hand with a broom. The old man beats Sally unconcious with the broom, uses the knife to cut some twine to tie her up, he then puts a gunny sack over her head and forcing her into his pickup truck. He drives her back to the dreaded house, and along the way picks up the hitch hiker from earlier in the day. They all live there, along with Leatherface. They tie Sally to a chair inside the house and remove the bag from her
head. She and the hitch hiker recognize one another and Sally screams in horror.
The family torments her for the rest of the night, forcing her to sit at their table while they eat a meal that is obviously made up of human flesh. They bring "Grandpa" down from upstairs, the dessicated old man, and slice Sally's finger open, sticking it in the old man's mouth while he sucks her blood. They tell Sally that "Grandpa" used to work in the
slaughterhouse and was the best with a sledgehammer there was. They decide to let Grandpa kill Sally and untie her, forcing her onto her knees and holding her head over a bucket while Grandpa makes several feeble attempts to hit her head with a hammer. The hitch hiker gets frustrated and makes a grab for the hammer to finish her off, and suddenly Sally breaks free. She hurls herself out a window again and lands outside just as dawn begins to break.
The hitchhiker and Leatherface emerge from the house and chase Sally up to the road, the hitch hiker brandishing a knife and Leatherface waving the chainsaw. The hitchhiker very nearly catches her, grabbing for her and catching her hair over and over. A large semi drives by and the hitch hiker is caught off guard; the truck drives over him, killing him. The truck driver slows down and gets out of the rig to see what happened, only to be confronted by a screaming, bloodied Sally with Leatherface close behind, the chainsaw buzzing. He chases Sally and the truck driver to the other side of the cab, when the driver hurls a wrench at him and hits him in the side of the head. Leatherface drops the saw and falls, wounded in the leg by the saw blade. The truck driver flees down the road, but the wounded Sally cannot catch up. Then a pickup truck drives by and Sally abandons the scene by jumping in the back of the truck. Leatherface still gives chase, but the pickup driver pulls away. Sally laughs crazily at Leatherface as she escapes, giggling at him as he swings his chainsaw around in frustration and rage in the middle of the road in the full light of dawn.