Season chicken pieces with salt and pepper. Heat butter and olive oil in a skillet over medium heat and brown the chicken in batches. Transfer to a plate. Add onion, celery, carrot, and garlic to pan and cook until translucent. Add anchovies, oregano, and bay leaves, and stir to combine.
Add browned chicken pieces back to pan. Add tomatoes, olives, wine, and chicken broth. Stir to coat chicken in vegetables and liquid. Turn heat down to low and cover pan. Continue cooking for 60 minutes, turning chicken periodically.
Serve hot with crusty bread and Radicchio orange salad (see recipe).
