Heat 2 tablespoons olive oil in a large frypan over medium heat. Stir in mushrooms and cook until soft. Remove to a plate.
Wipe out frypan and heat 2 tablespoons olive oil over medium-high heat. Place garlic, rosemary and chicken thighs in hot oil. Season with salt and pepper. Cook, turning chicken, until chicken and garlic are well browned.
Return mushrooms to frypan and sprinkle chilli flakes over chicken. Pour in white wine, scraping the bottom of the frypan with a wooden spoon. Cook about 3 minutes.
Reduce heat to low; cover, and simmer gently for 1 hour.
Sprinkle tomatoes and olives over chicken, return cover, and cook about 5 minutes more.