In the episode, on the Akritirian homeworld Tom Paris and Harry Kim are falsely accused of a terrorist bombing which kills 47 Akritirian citizens. They are sent to a brutal prison where inmates must fend for themselves to survive. When Captain Janeway tries to intercede, she is told by Ambassador Liri of Akritiri that Harry and Paris had confessed to the crime and her appeal for clemency is rejected. All the prisoners including Tom and Harry are implanted with a brain implant called "the clamp" which induces aggression among its victims. The apparent intent of the Akritirian's device was to cause the prisoners to fight and kill each other in order to reduce their numbers in prison thereby allowing the Akritirians to more easily control them.
An element of the prison sometimes drives prisoners insane. Harry must continually deal with changing prisoner loyalties, no secure place to actually bed down, devise a plan to escape and deal with Paris' mental affliction. The eponymous chute is a long, thin tunnel in which prisoners and food are dropped.
Whilst trying to defend Harry, Tom gets stabbed in the stomach. Harry takes him to the place where they sleep but someone had moved in there. Kim manages to work with one of the aliens in order to get bandages for Paris. Harry also tries to recruit the other prisoners into working together, but they just make fun of him. Harry and the alien he teamed up with find that the prison is actually a giant space station. Paris goes completely mad and wrecks a small device that Harry had been building. Harry, afflicted as well, attacks Paris in return but manages to hold on to his sanity.
Meanwhile, the Voyager crew manages to capture the real bombers—two people named Piri and Vel—who are linked with a terrorist group after locating their vessels and detaining their ships. When Janeway returns to the Akritiri and offers to exchange them for Harry and Paris, the Akritiri ambassador refuses, stressing that their convictions in the matter cannot be overturned. Janeway then approaches the bombers, who inform the Voyager staff that they know the location of the prison where Harry and Paris are kept. Janeway decides to free them in exchange for information on its location and on how to penetrate it.
Using Neelix's ship, which is still in the shuttlebay, they manage to hook into the chute—which is the only means to enter the prison. A small away team consisting of Janeway, Tuvok and a few security guards infiltrate the prison, pacify the prisoners and rescue Harry and Paris. They then quickly exit the scene just as an Akritiri patrol vessel states its intention to board Neelix's ship.
Back aboard Voyager, Harry is horrified at what he had almost done while afflicted. Paris convinces him to use a week's worth of replicator rations on recreating some of the meals they had discussed while in prison.