Halve leeks lengthwise and cut crosswise in 1 inch (2 cm) pieces.
Dry and season chicken with salt and pepper. Heat oil and 1 tablespoon butter in a skillet. Once hot place chicken and fry on both sides until golden. Remove chicken from skillet and set aside.
Add wine to skillet and bring to a boil over high heat. Deglaze skillet and reduce liquid to 3 to 4 tablespoons. Add leeks, remaining butter, salt and pepper and cook over low heat, covered, stirring frequently until leeks are soft. Stir in chicken stock and place chicken on leeks. Cook over low heat, covered until leeks are tender and chicken is just cooked through.
Remove chicken from the skillet and set aside. Stir in cream and bring to a boil over high heat, stirring, until mixture thickens slightly. Correct seasoning.
Serve chicken over leeks and sprinkle with chopped parsley.