Cut zucchini and yellow squash into 1/4-inch-thick slices; cut bell peppers into 2-inch pieces, and cut onions into small wedges.
Combine Italian dressing and next 3 ingredients; reserve 1/2 cup mixture to use later. Chill.
Place chicken in a shallow dish or zip-top plastic bag; add 1 3/4 cups dressing mixture, turning to coat. Cover or seal; chill 4 to 8 hours.
Place vegetables in a bowl; add remaining 1/2 cup dressing mixture, tossing to coat. Cover and chill 2 hours.
Drain vegetables, reserving marinade in bowl. Arrange vegetables in a grill basket.
Grill, covered with grill lid, over medium-high heat (350° to 400°) 15 minutes or until tender. Return half of vegetables to bowl, and toss with reserved marinade; keep warm. Cover and chill remaining vegetables.
Drain chicken; discard marinade.
Grill chicken, covered with grill lid, over medium-high heat (350° to 400°) 10 minutes on each side or until done. Serve 4 pieces with warm vegetables. Cover and chill remaining chicken.
Grilled Chicken on Greens: Toss 4 cups mixed salad greens with 1/4 cup reserved dressing mixture; arrange on individual plates. Cut remaining 2 grilled chicken breast halves into strips; cut 1 medium tomato into wedges. Place chicken and tomato on greens, and drizzle with remaining 1/4 cup reserved dressing mixture. Yield: 2 servings.
Summer Open-Faced Sandwiches: Cut 1 (12 inch) French bread loaf in half lenghwise; lightly toast bread. Drizzle cut sides with 1/4 cup reserved dressing mixture. Layer each half with 1 large tomato, thinly sliced; half of remaining grilled vegetables; and remaining 2 grilled chicken breast halves, cut into strips. Top with 4 mozzarella cheese slices. Broil 5 inches from heat (with electric oven door partially open) 2 minutes. Or wrap in aluminum foil, and grill, covered with grill lid, over medium-high heat (350° to 400°) 8 minutes. Halve each portion. Yield: 2 servings.