In a large saucepan, saute the onion, celery and garlic in butter until tender. Stir in the flour, sugar, salt, basil and pepper until blended. Gradually add broth; bring to a boil. Cook and stir for 1 minute; reduce heat. Add corn and cook for 5 minutes, stirring constantly. Stir in chicken. Pour into a greased 13-in. x 9-in. baking dish.
For dumplings, in a small bowl, combine baking mix and basil. Stir in milk with a fork until moistened. Drop by tablespoonfuls into 12 mounds over chicken mixture.
Bake, uncovered, at 350°F for 30 minutes. Cover and bake 10 minutes longer or until a toothpick inserted in a dumpling comes out clean.