Melt the butter with the oil in a large non-stick saucepan over a moderate heat. Add the chicken to the pan and sauté for 5 minutes until evenly browned all over. Remove the chicken and drain on paper towels.
Cut off the green parts of the leeks and set aside. Wash the white parts thoroughly, then slice thinly. Add the sliced leeks to the pan and fry for 5 minutes until soft.
Add the stock, rice and bouquet garni and return the chicken to the pan. Season to taste, then bring to the boil. Reduce the heat, cover and simmer for 30 minutes, or until the chicken is tender.
Slice the green parts of the leeks, then add to the pan with the prunes. Cover and simmer for a further 10 minutes.
Take out the bouquet garni, remove the chicken and shred the flesh into bite-size pieces, discarding the skin and bone. Return the chicken meat to the pan.
To serve, ladle the soup into warm bowls and scatter with some chopped fresh parsley or thyme.