Rimmer's chest was a wooden chest or trunk owned by Arnold Rimmer, and in which Rimmer kept his most prized possessions. It was the only thing that Rimmer's father had ever given to him, and had been in the Rimmer family for generations. Rimmer considered the chest and its contents as the only link to his early past.
After crash-landing Starbug on a snowy planet, Lister was forced to burn everything on board, in order to keep him from freezing to death. After burning everything, including the last copy of the complete works of Shakespeare, Lister and Rimmer have an argument about what will be burned next - Rimmer's Armée du Nord, or Lister's Guitar. It's a stalemate, since these are both of their most prized possessions.
Eventually, Lister seemingly concedes, saying that he will burn his guitar, only requesting that Rimmer allow him to play one more song on it. Rimmer agrees, but goes outside in the snow to avoid Lister's painfully off-key playing. Whilst Rimmer is outside, Lister hides the guitar in a locker, and cuts out a guitar shape of camphor wood from the back of Rimmer's chest, putting that into the fire instead.
Rimmer comes back in to see what he thinks is Lister's guitar burning in the fire, and is overwhelmed. Despite the fact his light bee can detect burning camphor wood, Rimmer doesn't realise and instead still thinks he's burned the guitar, and commends Lister on being a morally-upstanding guy and a good friend. In the name of friendship, Rimmer tells Lister to sacrifice the Armée du Nord to the fire too. As they burn, an upset Rimmer whistles military tunes, speaks goodbyes in French, and gives them the Rimmer Salute.
It was only being rescued by the Cat and Kryten with a Blue Midget that Rimmer caught on, as Lister went to retrieve the very-unburnt guitar from the locker, and Rimmer finally checked his chest. Seeing the guitar-shaped hole, Rimmer orders Kryten to get a hacksaw, and Kryten asks what for. Rimmer says that they're going to do to Lister, what Alexander the Great once did to me. ("Marooned", Series III)
- From playing with the Armée du Nord as a child, Rimmer had developed his fantasies of being a "romantic" general. As a youth, Rimmer had also been involved with the Io Amateur Wargamers. These fantasies of military command would come to fruition in the Series IV episode "Meltdown".
- Given the events of the Series X episode "The Beginning", it is likely that Rimmer also had his Holo-lamp in the chest.