The Royal House of Swayvill consists, from a legal standpoint, of King Swayvill, his wife, and all his direct heirs. At the moment, its only members are King Swayvill and his wife, Gieta.
King Swayvill the First
"It was a new portrait, of an old man seated upon a great throne. Tall and ancient, rail-thin, with dark eyes sunk so deep into a hollow, wrinkled face that they seemed to be staring back at me from within caverns... his hair and beard were long and white and wispy as fog. The corner of one lip curved in a sneer, exposing the sharp edges of his teeth. He wore red and gold and black, robes rich beyond compare. The Serpent Crown was upon his head, the Serpent Sceptre in his left, and in his right he held a great black-bladed sword by its golden hilt, pointed downward. Swayvill I, King of Chaos... it seemed as though the long turning of his years had scoured all weakness from him, along with his youth..."
Swayvill has ruled Chaos for centuries, coming to power in the wake of a brief civil war waged between several competing alliances of Houses after the death of the last king, Anbidian III. He entered into the alliance with Brand that saw Chaos waging open war with Amber, and, when Chaos was defeated in the Patternfall War, he put his signature on the peace treaty. He is a notably pragmatic king; he does not seem to have any fondness for Order or the royal family of Amber, but open war proved to be unfeasible, and so now there is peace.
Swayvill's health deteriorated greatly in the first decade following the Patternfall War, finally approaching the point where his death was assumed to be coming any day. Without a direct heir, various factions swung into action; there were many assassinations and, in a few cases, mass killings. Many of Swayvill's closest relatives died, some very unpleasantly.
Then came the news that Swayvill had died. The Lords and Ladies of Chaos gathered for his funeral, in Thelbane, ancestral home of all the Kings of Chaos since the Courts began...
They found a living, extremely healthy, and very unhappy Swayvill, and got to watch as a few dozen prominent House members were arrested before their eyes by Swayvill's Royal Guard and charged with various offenses relating to the assassinations of candidates for the throne. Many were convicted; some were executed, and some are still imprisoned.
It has never been certain whether or not Swayvill was truly ill and simply recovered, or whether he staged the entire thing as an exercise to root out possible threats to his rule. Or, as some occasionally whisper when they think it will not be traced back to him, to give himself an excuse to purge personal enemies and settle some long-standing grudges. Whatever the reasons, Swayvill I still rules in Chaos, and his power is as great as it has ever been, perhaps greater.
"...a tiny young woman, pale-haired and pale-eyed, wearing a plain dress of white and black, with a strand of pearls about her throat and a gold crown on her head. She seemed dwarfed by the rich splendour of the royal apartments she posed in, hands clasped in front of her, lips set in a nervous smile. She did not quite seem to believe she was there, being painted, wife of the King of Chaos..."
Swayvill married his current wife shortly after he recovered from his illness (or, by some interpretations, dropped the charade of it). There is much speculation as to why, as she comes from the tiny and insignificant House Phergon.
Some say it's because Phergon is so small that no one bothered to include it in any of the factions that tried to put their chosen candidate in place for the throne when Swayvill was apparently dying; thus, by marrying her, Swayvill showed no favour to any of the Houses involved. Some say that Swayvill fell in love with her beauty, which is not inconsiderable (though neither is it particularly stunning). Others whisper stranger things: that Gieta does not come from Chaos at all, that Gieta has miraculous powers of healing that saved Swayvill's life, that Gieta is a lost Princess of Amber, that Gieta a mighty Demon Lady who controls Swayvill as her puppet...
Whatever the truth is, Gieta very seldom appears in public except on ceremonial occassions, and has never even been known to speak. She accompanies her husband quietly, often seeming to move as though in a dream from which she is about to wake.