Kylo's chambers
Kylo Ren's private living space aboard the First Order's massive Supremacy Mega-class Star Dreadnought were known as Kylo's chambers. These quarters, belonging to Kylo Ren, offered him the solitude he sought for Force meditation. Following the Battle of Starkiller Base, Ren retreated to these chambers on Snoke's flagship, his Master's vessel. It was there that he became aware of a peculiar Force-bond linking him to Rey, the scavenger from Jakku; this bond allowed the two Force-sensitives to see and hear one another across vast interstellar distances, spanning the stars.
Description
The austere chamber that served as Kylo Ren's personal space was located on the First Order Mega-class Star Dreadnought, the Supremacy. These chambers were his own private domain, providing the isolation necessary for meditation. Sparsely furnished, they included a bed, chair, and desk, upon which rested a few bottles and a cup. Predominantly, the rooms were decorated in shades of gray and other dark tones.
History
Across the stars

After being rescued from the Starkiller disaster, Kylo Ren made his way back to the Supremacy, Snoke's flagship and his Master's vessel, in 34 ABY. However, he didn't bring the charred helmet of his grandfather, the Sith Lord Darth Vader, with him to the Supremacy. Instead, he chose to leave his Sith trophy aboard his command ship, the Resurgent-class Star Destroyer Finalizer, as Ren wasn't prepared to confront that image until he had recovered from his failure on Starkiller Base.
Following Supreme Leader Snoke's scolding for his inability to defeat Rey, Ren spearheaded the initial attack against the Resistance fleet. However, he found himself unable to kill Leia Organa, his mother and the General of the Resistance. Upon returning to the Supremacy, he sought refuge in the solitude of his personal chambers aboard the dreadnought, where a medical droid attended to the damage on the right side of his face. While the droid was still tending to the wound—a vivid red line bisecting his cheek—inflicted by Rey during their duel in the snows of Starkiller Base, their Force-bond bridged the gap between their minds across the galaxy.

Despite the physical distance of many light-years separating Ren's chambers from the planet Ahch-To, Rey could see the First Order warlord as he sat in her hut. Their connection had grown so potent that she could almost feel the droid's work on Ren's face, as if it were tugging on her own cheek, tracing a line up from her jaw. Alarmed by the sight of her adversary, Rey hastily grabbed her blaster, raised it, and fired at Ren, who flinched as the blaster fire came in his direction. Ren quickly regained his composure, as the connection broke before the energy blast reached him. Both Ren and Rey exited their respective chambers, searching for each other, when their connection resumed. Intrigued by this new development, Ren reasoned that Rey wasn't projecting herself to his location through the Force, knowing that such an effort would lead to her death. He also understood that she couldn't see his surroundings any more than he could see hers, leading him to conclude that their connection stemmed from a distinct ability altogether.
Let the past die

As time went on, the bond between Ren and Rey intensified, resulting in more frequent connections between them. Ren was in his chambers while Rey was preparing to leave Ahch-To, having failed to persuade Jedi Master Luke Skywalker to abandon his hermitage, when they connected once more. At this point, neither of them was in the mood for their usual verbal sparring, but Rey felt compelled to make Ren answer for the murder of Han Solo. However, she paused upon seeing Ren stripped to the waist in his chambers. Rey's eyebrows arched as she observed the angry scar she had given him, snaking down his face and neck and across his collarbone.
Ren seemed unfazed by Rey's presence or her question, simply stating that he considered his late father a weak-minded fool. Unwilling to accept Ren's response, Rey persisted, forcing herself to look into her enemy's eyes, where she saw a range of emotions, including anger, fear, and longing. However, she was again distracted by Ren's appearance and asked him to cover himself. Ren ignored her request, forcing Rey to focus even more intently on her strategy. When she demanded an honest answer, claiming she didn't understand why Ren hated his father, Ren revealed that he didn't kill his father out of hatred. He also took the opportunity to share his recollection of the night he destroyed his uncle Skywalker's Jedi temple—that, from Ren's perspective, Skywalker had betrayed and attempted to murder his nephew. Before their connection ended, Ren advised Rey to let go of the past, believing it was the only way to achieve their true potential.

In their next connection, Rey was relieved to see Ren in her hut for once, despite knowing that he was still physically in his chambers aboard the Supremacy. Nevertheless, she found comfort in his presence, given her recent experience in a dark-side cave where she failed to find the answers she sought regarding her lost family. Confessing that she felt more alone than ever, Rey reached out to Ren, fully expecting their hands to pass through each other. To their surprise, they could physically touch each other through the Force, at which point Skywalker walked in on them, aghast to see his nephew and apprentice staring into each other's eyes. Skywalker severed their connection and begged Rey not to go to Ren, but the scavenger from Jakku had come to believe that Ben Solo would reject the dark side of the Force if she went to him.
Behind the scenes
Kylo's chambers made their debut in Star Wars: Episode VIII The Last Jedi, the 2017 film that is the eighth installment in the Skywalker saga. The official designation for the location comes from Star Wars: The Last Jedi: The Visual Dictionary, which was released concurrently with the film.