Preheat the oven to 375 degrees.
Clean chicken parts and remove skin. Pat dry with paper towels and season with salt and pepper.
Heat one tablespoons olive oil and one tablespoons butter in a large, oven-safe skillet. Cook the chicken pieces over medium-high heat until nicely browned. Remove browned chicken to a platter and keep warm.
Heat the remaining tablespoons olive oil and tablespoons of butter. Add the onions and mushrooms to the skillet and saute until the onions are translucent and the mushrooms are tender, about 5 minutes.
Add 2 tablespoons flour to mushrooms and onions and cook while stirring, about a minute.
Add broth and wine to skillet and simmer uncovered, stirring occasionally until sauce thickens and reduces, about 5 minutes.
Return chicken to the skillet (with the juices from platter), add artichokes, and cover. You can also transfer to a heat-safe casserole dish if you don't have an oven safe skillet. Bake at 375 degrees for 40 minutes.
Re-season with salt and freshly ground black pepper to taste before serving.