Pour broth into a large, wide saucepan and set over medium-high heat. Stir in seasonings and garlic. Add onions and carrots to broth. Cover and reduce heat to medium-low. Boil gently until carrots begin to soften slightly, about 5 minute.
Stir zucchini and chicken into broth. Then stir into broth with sugar, raisins and apricots. Increase heat to medium. Cover and cook, stirring occasionally, until chicken is springy when pressed, 7 to 10 minute.