In the episode, Tom Paris and Harry Kim are accused of terrorist atrocities on the Akritirian homeworld and sent to a brutal prison where inmates fend for themselves.
An element of the prison sometimes drives prisoners insane. Kim must deal with changing loyalties, no place to actually bed down, a plan to escape and 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.
Kim also tries to recruit the other prisoners into working together, but they just make fun of him. Kim 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 Kim had been building. Kim, afflicted as well, attacks Paris in return but manages to hold onto his sanity.
The Voyager crew manages to track down the prison. Using Neelix's ship, which is still in the shuttlebay, they manage to hook into the chute. A small Away team consisting of Janeway, Tuvok and a few security guards pacify the prisoners and rescue Kim and Paris.
Back on board, Kim 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.
The plot of this episode bears several striking similarities with the Lois McMaster Bujold short story, Borders of Infinity.