Add fermented black beans into a bowl and water to cover. Gently wash the beans by hand, rinse a few times, drain, and transfer to a small bowl. Mash with the back of a spoon.
Add the rest of the ingredients. Stir to combine.
Dry chicken breasts with paper towel. Transfer to a large zipper bag. Pour in sauce, use a spoon to arrange the sauce, so the marinade is on the meat side of the chicken. Squeeze out as much air as possible and seal the bag. Massage the bag a few times. Let marinate for 30 minutes to 1 hour. If you aren’t going to cook the chicken immediately, you can store the chicken in the fridge for 2 to 3 hours.
Light one chimney full of charcoal. When the charcoal at the top of the chimney is lit, put on heat resistant gloves, and pour the charcoal halfway over the coal grate to create a moderate two-zone fire. Set the cooking grate in place, cover the grill, and preheat for 5 minutes. Clean the cooking grate. Use a pair of tongs to dip a paper towel in oil, and brush grate with a thin layer of oil. Skip this step if you’re using a skin-on cut.
Place chicken breasts on hottest part of the cooking grate, skin side down. Grill uncovered until the bottom is browned, about 3 minutes. Flip to cook the other side until browned.
Transfer the chicken breasts to the cooler part of the grill, skin side up. Cover and cook for 10 minutes. Flip and cook covered again, until the internal temperature of the thickest part reads 68 degrees C (155 F). Remove chicken from the grill and let rest for 5 minutes. The residual heat will continue to cook the chicken a bit more.
Serve warm or at room temperature with rice and grilled vegetables, or over salad.