The Chamber of Repose and the Chamber of Waking are mysterious rooms that seem to hold some great importance to Xemnas, due to their connections to his past. Xemnas often sits in the Chamber of Repose in order to regain memories of his past as Terra and Master Xehanort, and seeks the Chamber of Waking in Kingdom Hearts 358/2 Days, Kingdom Hearts II Final Mix and Kingdom Hearts 0.2 Birth by Sleep -A fragmentary passage-.
I know it's a lonely place, but you'll be safe. Terra and I will be back to wake you up before you know it.
Aqua to a comatose Ventus
In Kingdom Hearts Birth by Sleep, following Ventus entering a coma-like state, Aqua transforms the Land of Departure into Castle Oblivion. The throne room of Land of Departure becomes a chamber that looks very similar to the Chamber of Repose, only instead of Nobody sigils, the room is adorned with the Keyblade Master symbol, and the room is noticeably brighter. There is a single, tall throne in the center, where Aqua lays the comatose Ventus.
The Chamber of Waking contains Xemnas's other "friend", Ventus. This room is found in Castle Oblivion. Whether or not Xemnas ever found this room is unknown, although based on conversations between Saïx and Axel in Kingdom Hearts 358/2 Days, it is unlikely that Xemnas has, since Axel was ordered to search for the room after he had disposed of the Organization's traitors, but failed to find such a room.
After the apprentices banished Ansem, but before they became Nobodies, the apprentices created the Chamber of Repose within the Radiant Garden's castle. Xemnas would frequently travel to the room, as if something within it reminded him of his forgotten past. In the scene in Kingdom Hearts II Final Mix, Xemnas entered Ansem's computer room, inserted a data disk into the machine, and typed in the password "Another", after which he typed in six more passwords: the original names of the six apprentices.
This caused a passage to appear below the Heartless Manufactory, which had a long stairway spiraling down to a long hall. Inside this hall were doors electronically locked and bound with chains. At the end of the hall was a room containing a throne for Xemnas to sit on, as well as the armor and Keyblade of a warrior named Aqua. Xemnas would speak to the armor, addressing it as a "friend".
Apparently, Xigbar often eavesdropped on the conversations and told Zexion that he heard another voice once. He also told Zexion he suspected that there was a link between the Chamber of Repose and Castle Oblivion, where, allegedly, the Chamber of Waking is.
Kingdom Hearts 0.2 Birth by Sleep -A fragmentary passage-
During the chapter "Reunion", at the end of the visit to Enchanted Dominion, there is a conversation between Aqua and a version of Terra. While talking about Ventus's condition, Terra suddenly transforms into Terra-Xehanort and asks about the Chamber of Waking.
Though the chamber itself does not appear, in the opening movie of Kingdom Hearts Re:coded, Ventus is briefly seen sleeping in the Chamber of Waking.
At the end of Kingdom Hearts 3D: Dream Drop Distance, Ventus is briefly seen in the Chamber of Waking. He continues to sleep on in the chamber, but can be seen wearing a slight smile.