Hakkai was born Gonou. He was orphaned in his childhood and he and his sister Kanan were raised in separate orphanages. Gonou was a solemn little boy who never smiled, missing Kanan, his other half, intensely. Sometime after they left their respective orphanages they met again and became lovers, both happy that they weren't alone any more and not especially worried about issues like incest. (This detail gets cut from the anime.) They moved to a small village and Gonou became a school teacher. One day he was out playing with his kids after school and came home to find the house a shambles and Kanan gone. There was a tribe of youkai led by Hyakugan Maoh (hundred/ eyes/ demon/ king) who used to go on 'women hunts'- finding women for Hyakugan Maoh's bed. They'd come to the village and were going to take some of the village women but the villagers offered them Kanan instead. (Hyakugan Maoh shows up in connection with another character, who says that it's H's custom to use the women for sexual sport and eat them when he's tired of them. Not a nice man. Is also a centipede of some sort feh.)
Gonou had said he'd protect Kanan from the world, but not only had he not been able 
to do that, he hadn't even realized she was in danger. No evidence as to what was going on in his mind at that point- all we *know* is that he went on a rampage and killed half the men of the village. Gonou went after Hyakugan Maoh and apparently took some time getting to his castle, because it was two months later that he got there, killed the whole tribe of youkai, and found Kanan still alive imprisoned in the dungeon. When he rushed to the bars of her cell to free her, Kanan pulled Gonou's knife out of his belt and said he was too late to rescue her. She told him she'd become pregnant by Hyakugan Maoh, and then stabbed herself.
Enter at this point the jaded youkai, son of Hyakugan Maoh, whose original name we don't know but who later calls himself Chin Isou. Isou had apparently just wandered back in to find his entire family dead. This fact he finds mildly interesting, and so tracks the murderer down to the dungeons in time to witness the scene with Kanan. Gonou intrigues him, as evidently nothing has intrigued him in several centuries- ahh being a youkai prince is so dull, you just can't conceive of the ennui, my dear- and he decides to try a little experiment. There's a saying that if a human bathes in the blood of thousand youkai he becomes youkai himself, and well-well could it be possible that Isou is the 1,000th youkai let's just nick a vein here and dribble it over him and see what happens. What happens is that Gonou becomes youkai and does something messy to Chin Isou.
Gonou then stumbled out into the night and was sometime later discovered by Gojou. Hovering on the brink of death, he says he was pulled back by the sight of Gojou's red hair that acted as a sign to remind him of the crime he'd committed. He stayed at Gojou's a month and then prepared to leave, intending to return to Hyakugan Maoh's castle and bury Kanan's body before giving himself up to the authorities. Sanzou, sent to find Gonou by the three Buddhist divinities, showed up at Gojou's door before Gonou could leave. After a fight, Gonou fled into the night, carrying Sanzou's gun that he'd picked up in the course of the fight.
On the way to the castle Gonou is stopped by a man from his old village, seeking revenge for what Gonou did- specifically for the fact that Gonou gouged his brother's eyes out. Gonou happily agrees to make recompense, and gouges out his right eye. He's about to take out the left one as well when Gokuu jumps on him and stops him. Evidence on this right eye is contradictory. Minekura says in vol. 1 that he can hardly see out of it; in vol.5 he actually gouges the thing out so it flies through the air. Why Hakkai then wears a kind of half-spectacles in front of it is anyone's guess. Because it looks cool, I bet. Sanzou, Gojou and Gokuu accompany Gonou to Hyakugan Maoh's castle, only to find that it had been burned to the ground some days before by someone unknown and that nothing at all remains. Sanzou takes Gonou back to be judged for his crime by the Buddhist divinities, and later tells Gojou that Gonou is dead. That's 'dead' in some religious sense, because Gonou is still alive, but has changed his name to Cho Hakkai. Hakkai moves back in with Gojou, who needs his domestic presence. 'He can't even remember when garbage days are.'
Hakkai has three earcuffs, worn in the left ear, which keep him in his human form. His youkai form, the one view we've seen of it (left) is kind of pretty if you don't count the claws. (Those are leaves, by the way, not baseball stitchings.) Suggestion however is that he's not entirely sane when in youkai form. When he changes over in vol.7 to get rid of a large black thing with teeth, he tells Gokuu to stand well out of the way 'or else I might kill you.' On the other hand, as someone pointed out, he's able to find and reattach his earcuffs afterwards when the threat is over.
Perpetually smiling, patient, reasonable and soft-spoken, with his feelings well-hidden on the inside in a perfect exemplar of the Japanese word enryo (holding back out of politeness), Hakkai is a difficult character to fathom. He gives very little away; and when, under extreme duress, angst over his past comes to the surface, Sanzou is usually there to tell him to stop. Sanzou's view is that having killed a thousand youkai and half a village is nothing to lose sleep over. Just part of life. Whether Hakkai agrees or not- well, who knows? Hakkai's method of fighting is the most peaceable of the three youkais'. He concentrates his ki (vital energy) to form protective barriers and so on. Nonetheless the impression remains (something to do with the systematic destruction of a tribe of youkai, perhaps?) that Hakkai is potentially the most dangerous of the lot under that calm surface.
Hakkai owns a little white dragon, Jiipu in the manga and Hakuryuu in the anime, who at need turns into- what else?- a jeep. Evidently Jiipu too was once a celestial up in heaven.