Combine flour, salt, and pepper on a plate or shallow dish. Stir well. Dredge* chicken pieces in the flour mixture to coat all sides well.
Heat oil and butter in skillet over medium heat, then add chicken pieces. Brown on both sides, about 4 minutes each side.
While chicken browns, mince shallot to yield about 1/4 cup. Chop tomatoes to yield about 2 cups. Slice fresh mushrooms (or use frozen, sliced mushrooms).
When chicken has properly browned, remove from skillet, place on a clean plate, and keep warm.
Add shallots, tomatoes, and mushrooms to the juices in the skillet. Turn heat to medium low and cook 2 to 3 minutes, stirring frequently.
Slice pitted green olives, then add to vegetables along with wine, thyme, salt, and pepper. Cook and stir another minute.
Transfer chicken back to the skillet, nestling the pieces into the sauce, but not covering them with the sauce. Cover skillet with a lid or aluminum foil. Turn heat down to keep at a simmer. Cook 30 minutes. Remove lid and cook another 5 to 10 minutes to reduce sauce if desired.
When serving, place chicken on a plate (or rice, etc.), then cover with some sauce.