Place the chicken breasts into a slow cooker, and pour in the kidney beans, pinto beans, black beans, onions, green bell pepper, tomato paste, brown sugar, rice vinegar, chili black bean sauce, and sea salt. Stir to combine all ingredients, and set the cooker to High. Cook for 1 hour; stir again, and set the cooker to Low. Cook for 4 more hours.
Remove the chicken breasts, shred with 2 forks, and stir the shredded chicken back into the chili. Sprinkle the top of the chili with Cheddar cheese, and serve.