Place chicken in the Instant Pot(R) and cook for 10 minutes on the 'Manual' setting. Release pressure naturally according to manufacturer's instructions.
Set the pot to 'Saute' and add green bell peppers, yellow onion, soy sauce, brown sugar, honey, garlic, and black pepper. Cook until most liquid is evaporated, vegetables are soft, and chicken is no longer pink in the center, about 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
