Heat 2 tablespoons olive oil, 2 turns of the pan, in a large Dutch oven over medium-high heat. Season the chicken pieces with salt and pepper, and brown evenly on both sides, about 7-8 minutes total; remove to a plate. Deglaze the pan with wine and evaporate to 2-3 tablespoons; pour over chicken.
Add more olive oil to pan, 2 turns of the pan along with red onion, celery, carrots, potatoes, garlic, salt, pepper and chili pepper. Partially cover pan and stir occasionally to soften, 6-8 minutes. Add roasted peppers, tomatoes, olives, capers, vinegar, honey, basil, parsley and bring to bubble. Slide chicken and juices back in and simmer to cook through, 20 minutes at low bubble.