Chop the onion and bell peppers, mince the garlic, and cut the chicken into 1-inch pieces, seasoning it with salt and pepper. Drain and rinse both the kidney and black beans.

Heat oil in a large pot over medium heat, then add chopped onion and cook for 5-7 minutes until soft. Stir in minced garlic and cook for another minute until fragrant, being careful not to brown it.

Push the onions and garlic to one side, add seasoned chicken pieces in a single layer, and cook for 3-5 minutes per side until lightly browned. Remove the chicken and set it aside.

Add the chopped bell peppers to the pot and cook for 5 minutes until softened. Stir in the chili powder, cumin, smoked paprika, oregano, and cayenne pepper, cooking for 1-2 minutes while stirring constantly to toast the spices.

Return the browned chicken to the pot, then pour in the chicken broth, diced tomatoes, crushed tomatoes, diced green chilies, kidney beans, and black beans. Stir in the salt, black pepper, cocoa powder, apple cider vinegar, and brown sugar, then bring the chili to a boil. Reduce heat to low, cover, and simmer for at least 1 hour (up to 2-3 hours) for best flavor development, stirring occasionally.

Taste the chili and adjust seasonings as needed, adding more salt, pepper, or chili powder. If the chili is too thin, simmer it uncovered to reduce, or stir in a cornstarch slurry (1 tbsp cornstarch mixed with 1 tbsp cold water) until thickened.