Chaos Bahamut (バハムート・カオス, Bahamūto Kaosu?) is the Eidolon incarnation of Caius Ballad, which he transforms into by performing incarnate summoning. It first appeared as an alternate boss form to Caius in Final Fantasy XIII-2.
It is a darker palette swap of Fang's Bahamut from Final Fantasy XIII, the difference being that the wings are always present on Chaos Bahamut, whereas they only manifested in Gestalt Mode in Final Fantasy XIII. Chaos Bahamut is named after the destructive substance known as chaos, a formless mass of dark energy that exists in the unseen realm. Caius has mastery over the forces of chaos due to a gift given to him by the goddess Etro, the Heart of Chaos. It being a "dark" form of Bahamut makes it somewhat akin to the Dark Aeons from Final Fantasy X.
Chaos Bahamut appears as a boss that first appears in the pregame tutorial. Its main appearance is at the end of Academia 500 AF. Chaos Bahamut is also fought in the DLC episode Requiem of the Goddess.
Caius is a Guardian to seeress Paddra Nsu-Yeul from hundreds of years ago. He performed an incarnate summon to destroy an enemy force, a skill that let him become one with his Eidolon, but would cost him his life. The goddess Etro, moved by Caius's dedication, freed him from his fate as a l'Cie and infused her heart, the Heart of Chaos, into his body, making him immortal so he could protect every incarnation of Yeul until the end of time. From this day on, Caius could perform incarnate summon to become Chaos Bahamut at will. Although given as an act of benevolence, Caius would come to see his eternal life as a curse due to the madness he would have to endure, and develops a plan to kill the goddess in Valhalla where she resides to free both himself and Yeul from their fates.
When Caius challenges goddess Etro's protector Lightning to battle, he transforms into Chaos Bahamut and sends Lightning flying as they continue their duel. After Lightning saves a falling Noel by riding her own Bahamut, Caius pursues the two in the form of Chaos Bahamut and engages her in an aerial dogfight. Lightning defeats him, but he reappears and summons a meteor above the temple of the goddess. Lightning asks Noel to bring her sister, Serah, to Valhalla, and sends him through a Time Gate to New Bodhum 3 AF where Noel will begin his journey through time with her.
Serah and Noel eventually make their way to Academia in 500 AF, the time when Caius plans to destroy both the old and new Cocoons to unleash Valhalla's chaos onto the mortal realm. Serah and Noel chase after Caius into the sky on an airship and defeat him as Chaos Bahamut. Caius returns to human form and reaffirms he will stop at nothing to free Yeul even if reality itself must be destroyed to achieve it. He transforms into Chaos Bahamut and flies into a wormhole that opens in the sky.
Noel and Serah follow Caius into the wormhole and emerge in Valhalla where Caius confronts them and uses the chaos of Valhalla to transform into Jet Bahamut but is defeated along with his supporters, Garnet Bahamut and Amber Bahamut. Having lost the final battle, a weakened Caius returns to human form and fades away after making Noel pierce his Heart of Chaos.
Able to appear at the beckoning of the Chaos Yeuls, Caius, who has become part of the chaos itself, is summoned to fight Lightning when she attempts to rescue Serah's soul in the "Requiem of the Goddess" DLC scenario. Though defeated even if he transforms into Chaos Bahamut again, Caius's existence continues as the boundaries between the mortal and unseen realm mingle.
Chaos Bahamut accompanies Caius in battle and is capable of performing powerful attacks at his master's beckon. Caius no longer directly transforms into it.
Chaos Bahamut appeared for "a special event".
Chaos is "the formless matter supposed to have existed before the creation of the universe."
Bahamut (Arabic بهموت Bahamūt) originated as an enormous whale in ancient pre-Islamic Arabian mythology. Upon Bahamut's back stands a bull with four thousand eyes, ears, noses, mouths, tongues and feet called Kujuta (also spelled "Kuyutha"). Between each of these is a distance of a 500-year journey. On the back of Kujuta is a mountain of ruby. Atop this mountain is an angel who carries six hells, earth, and seven heavens on its shoulders.
Another version of the Arabic story is that Bahamut is indeed a dragon and he stands on a whale called Liwash.
In modern times, the game Dungeons & Dragons is responsible for re-imagining Bahamut as the king of dragons, a benevolent Platinum Dragon; the opposite of the malevolent Tiamat, the five-headed Chromatic Queen of Dragons.