Plateau, a colony in the Tau Ceti system, was settled by humans some 300 years before the plot begins. The colony world itself is a Venusian type planet with a dense, hot, poisonous atmosphere. It would be otherwise uninhabitable, except for a tall monolithic mesa that rises 40 miles up into a breathable layer in the upper atmosphere. This gives the planet a habitable area about half the size of California. The Captain of the first colony vessel named the feature Mount Lookitthat (from his interjection at first sight of it), and the colony became known as Plateau.
After landing the slower-than-light ships, the Crew sign an agreement, called the Covenant of Planetfall, with their former passengers (who had just emerged from suspended animation and were in a weak bargaining position). This agreement gives the Crew (and their descendants in perpetuity) all control over the new colony. A system of medical care evolves, in which organ transplantation is the only method of treatment, even for cosmetic defects (such as baldness); a justice system evolves, with all crimes punishable by death, followed by involuntary donation of the decedent's transplantable organs (including skin, scalp, and teeth). Not surprisingly, only Colonists are ever arrested for crimes; and only Crew are eligible to receive transplants. Some Colonists become dissatisfied with the system and form a dissident group called the "Sons of Earth."
The prologue of the story begins with a dissident Colonist escaping Implementation, the local police force, by jumping to his death over the "void edge", the 40 mile high cliff that forms the sides of the mesa. On Mount Lookitthat, all crimes are punished by being dissected for spare parts. Thus, this is considered to be the greatest of all possible crimes, as it leaves nothing to harvest.
An automated Bussard ramjet arrives from Earth, carrying an unknown cargo of great importance, which the government immediately finds and conceals, but not before the cargo has been observed and photographed by Polly, an agent of the Sons of Earth.
Meanwhile, Matthew Keller, an ordinary miner, gets casually invited to a party and is drawn into a conversation about psi powers. Matt strikes up a flirtatious conversation with Polly, but she suddenly loses interest. Angered, Matt hooks up with a woman named Laney and is in the middle of having sex with her (his first time) when Implementation agents raid the house, which turns out to be full of Sons of Earth members. Matt manages to escape in a stolen car. The Implementation chase him to the edge of the Plateau where he dives into the poisonous gas. The Implementation leave him for dead, but he manages to survive and resurface.
Feeling guilty, he makes an attempt to enter the Hospital where the captured Sons of Earth have been taken and rescue Laney. He has several strange encounters with the Implementation where they suddenly fail to be able to see him. He makes his way to the vivarium, where those of the Sons of Earth who are still living are being kept, and sets them free. He, along with two of the leaders and Laney, steal another car and flee to the home of Millard Parlette, a prominent political figure and direct descendant of the captain of the original colony vessel.
Matt explains to them how he rescued them and they conclude that he has a psionic power: the ability to influence the optic nerves of anyone whose attention is focused on him. When he is excited or frightened, people focused on him are compelled to contract the pupils of their eyes, and thereby lose that focus to the point of short-term memory loss – even if he has just threatened them with a weapon.
When Millard Parlette returns home, he allows himself to be captured by Matt with little difficulty. However, the others overreact upon seeing him enter the house and knock him out with a stun gun. Matt and Laney leave to go back to the hospital. Matt intends to rescue Polly, having realized that her rejection of him was an outcome of his nervousness and psionic power. Laney intends to rescue the rest of the Sons of Earth who were recaptured.
In the house, Millard Parlette reveals what the cargoes of the ramship were. They consist of four medical breakthroughs: a symbiote that regenerates skin, technology to culture a human liver, another to culture a human heart, and a second symbiote that lives in the bloodstream and grants many benefits: it fights disease, dissolves blood clots, repairs and cleans fatty deposits from the circulatory system, and maintains hormone levels at those of an adult. These advancements are amazingly beneficial, but that is the precise problem. Colonists, once they learn of them, would assume that the organ banks had become obsolete, and expect Implementation to disband. However, these advancements only reduce the need for transplants, they do not remove it. But when Implementation continues to take colonists to the banks, they would assume that necessity had given way to malevolence. Every colonist on Plateau would revolt. At least half the population would perish in the conflict, and technological civilization might come to an end. Thus, the political figure wants to negotiate a replacement for the Covenant of Planetfall with the rebels in advance, and thereby prevent such a conflict.
Though the rebels are perfectly willing to deal, there is still one significant problem: Implementation. Any settlement with the Colonists would involve reducing the power of the Crew's police force. As such, Implementation would be on the side of the conservative Crew faction, those who would die before accepting a compromise with those they currently hold the power of life and death over. And Implementation controls the best weapons on Plateau. It is led by a man named Jesus Pietro Castro and is headquartered in the Hospital, which is constructed around the two immense "slowboat" spacecraft which had brought them there.
Meanwhile, Matt and Laney are able to enter the facility with no real problem. Matt tricks Castro into leading him to where they are keeping Polly and Matt sets her free. However, this turns out to be a mistake: Implementation was interrogating her via sensory deprivation, and she is now insane. He makes love to her and in so doing restores her ability to function. But when she learns of their location, she is gripped with a fanatical devotion to the cause of the Sons of Earth. She flees Matt, intending to detonate the nuclear reactor on one of the slowboats, to destroy the Hospital and kill as many Crew as she possibly can. She is unable to reach the reactor and instead settles for the ship's long-defunct control room. She then ignites the ship's landing motors; this severely damages the Hospital, kills many of the crew, and thrusts the ship off the "void edge" to its destruction. Matt manages to jump from the ship before she does so.
Thus war is averted. The new government, led by Millard Parlette, has assumed control of the Crew. And on the Colonists' side, the rebels have claimed control of the most powerful weapon on Plateau: Matt Keller. The Sons of Earth threaten to use Keller to assassinate Millard Parlette if he becomes too power-hungry. Keller accepts this, but demands a position of power among the rebels. And he's just discovered a new wrinkle in his power. Not only can he compel someone to lose focus on him, he can compel someone to intensify that focus, putting them in a hypnotic trance, which is implied to make him the true master of Plateau.
As the story began with a robot ramship in flight, it ends with another ramship headed from Earth to the human colony known as 'We Made It' (in the Procyon system) with the same discovery. This ship is observed by alien Outsiders, who follow it in hopes of selling faster than light technology to the locals. This sale will lead to the advanced multi-species society portrayed in Neutron Star and Ringworld.