In a large pan, combine stock and bouqet garni, cover and bring to the boil. Add chicken, carrot, celery and rice. Reduce heat to medium, simmer until chicken is cooked, about 10 minutes. Using a slotted spoon, remove chicken, transfer to a plate to cool.
Reduce heat to low, simmer until rice is tender, about 10 minutes. While the soup is cooking, dice chicken, set aside.
Add mushrooms and peas to the soup, simmer for 5 minutes. Remove bouquet garni. Stir in chicken, parsley and pepper. Ladle the soup into bowls, serve.