Pat the chicken dry. In a large skillet, melt the butter over high heat. Add the chicken and sauté, turning once, until browned, about 2 minutes on each side. Add the onions and cook until golden, about 3 minutes.
Stir in the flour. Reduce the heat to moderate and cook until the flour is light brown, 3 to 5 minutes.
Add the shallots, garlic, wine, stock, tomato paste, bouquet garni, salt, pepper and thyme. Cover, reduce the heat to moderately low and simmer, skimming the fat from the surface of the sauce several times until the chicken is tender, 25-35 minutes. Remove the bouquet garni.
Meanwhile, put the green olives in a medium saucepan, cover with cold water and bring to a boil. Strain and rinse under cold water. Repeat this blanching process 2 more times. Black olives are not usually as salty as the green ones, but if they, blanch them also.
In a large skillet, heat the oil over high heat. Add the mushrooms and sauté, tossing, until browned, about 3 minutes. Season with additional salt and pepper to taste.
Shortly before serving, add the olives, mushrooms and tomatoes to the chicken. Simmer for 5 minutes. Garnish with chopped parsley.