Combine first 9 ingredients in a small bowl, stirring well. Toss cabbage and lettuce with half of dressing mixture in a large shallow bowl. SPrinkle walnuts over cabbage mixture.
Combine chicken and 3 tablespoons remaining dressing mixture in a skillet over medium heat. Cook, stirring occasionally, until chicken is thoroughly heated. Toss hot chicken mixture and grape halves with cabbage mixture. Serve salad warm with remaining dressing.