Cut off tall stalks and feathery leaves from fennel bulb; rinse well and cut in half. Reserve 2 tablespoons minced fennel leaves. Trim base from fennel bulb; remove tough outer layers. Slice fennel hearts crosswise to form celery-like pieces. Measure 1/2 cup; set aside. Place chicken, fennel stalks and remaining leaves in a large pot; cover with water. Bring to a boil; skim the top. Reduce heat and simmer 25 minutes or until done. Remove chicken from the broth; cool partially. Pull meat from the bones; cut into small chunks. In a medium bowl combine mayonnaise, reserved minced fennel leaves and chives. Mix in chicken, sliced fennel and walnuts. Season with salt and pepper.