Rinse chicken with cold water, and place in a large Dutch oven. Add milk, water, salt, and 1/2 teaspoon pepper; simmer over low heat 30 minutes. Remove chicken from broth, reserving 1 cup broth. Remove skin from chicken, and set aside.
Melt butter over low heat; add flour, mace, and 1/4 teaspoon pepper. Stir until smooth. Cook 1 minute, stirring constantly. Gradually add reserved broth and whipping cream; cook over medium heat, stirring constantly, until thickened and bubbly. Serve chicken on a bed of rice. Spoon white sauce over chicken.