Heat olive oil and butter in a large stock pot or saucepan over medium heat.
Add chicken, skin side down, to the heated oil and brown chicken on each side until golden. Work in batches so that the chicken isn't overcrowded.
Remove chicken from the skillet and set aside. Add onions, bell peppers, and sliced mushrooms to the pan and cook until softened.
Add the minced garlic and saute 1-2 minutes longer.
Deglaze the pan by adding the sherry (or wine) and simmering, scraping the brown bits from the bottom of the pan.
Add basil, oregano, tomatoes (juices included) and chicken broth. Stir to combine.
Add the chicken back into the pan, nestling it down into the sauce. Bring the sauce to a simmer and then reduce the heat to low. Cover and cook 30 minutes more.