1. Stir together the yogurt and dressing mix in a large bowl until well blended. Fold in chicken pieces until well coated. Cover; marinate at room temperature for 15 minutes.
2. Heat broiler. On each skewer, alternately thread 4 pieces chicken, 4 pieces zucchini, and 4 cherry tomatoes. Brush zucchini and tomatoes with some of remaining yogurt mixture. Place skewers on broiler pan.
3. Broil skewers 5 inches from heat for 25 minutes or until browned and chicken pieces register 160 degrees F on instant-read thermometer; turn skewers over once about halfway through cooking, and brush with yogurt mixture.