Season chicken with salt and pepper. In a large saucepan cook and stir chicken in hot oil 2 minutes or until browned. Sprinkle flour and marjoram over chicken. Stir in broth, vegetables, and water. Bring to boiling; reduce heat. Simmer, covered, 5 minutes.
In a mixing bowl combine biscuit mix, cornmeal, and cheese. Stir in milk just until mixture is moistened. Drop batter by spoonfuls onto hot liquid, making 8 dumplings. Return to boiling; reduce heat. Simmer, covered, for 10 to 12 minutes until dumplings test done. (Do not lift cover while simmering.) Makes 4 servings.