1. In a large frying pan, place oil and heat to medium temperature. Add chicken, onion and garlic; cook about 10 minutes or until chicken is brown on all sides. Remove chicken and set aside.
2. To same pan, add tomatoes, wine and thyme.
3. Remove skin from chicken and return to pan. Add salt, pepper, mushrooms and 1/2 of the parsley. Cook about 20 minutes longer or until fork can be inserted in chicken with ease.
4. Place 1 slice of cheese on each breast half, sprinkle with remaining parsley, cover and simmer until cheese melts.