In a large pot or Dutch oven, heat olive oil over medium heat. Brown the chicken pieces on all sides (about 3-5 minutes per side). You may need to do this in batches. Remove the chicken and set aside.

In the same pot, sauté the chopped onion until translucent, about 3 minutes. Add the minced garlic and cook until fragrant, about 1 minute more.

Return the browned chicken to the pot. Pour in the soy sauce and vinegar. Add the bay leaf and whole peppercorns. Bring to a simmer, then reduce heat to low, cover, and let it cook for 15 minutes.

Stir in the tomato sauce and water (or broth). Add the cubed potatoes and sliced carrots. Bring the liquid back to a gentle boil, then reduce heat, cover, and simmer for another 20 minutes, or until the chicken is tender and the vegetables are cooked through.

Add the sliced red bell pepper and cook for an additional 5 minutes, uncovered, to allow the sauce to thicken slightly. Taste and adjust seasoning with salt and pepper as needed.

Remove the bay leaf before serving. Serve hot over steamed white rice.