Place chicken in large resealable plastic bag; add vinaigrette dressing. Seal bag; turn to coat. Refrigerate for 30 minutes, turning bag halfway through.

Cut cucumber in half crosswise. Using a vegetable peeler, cut one half into thin ribbons; set aside. Coarsely shred remaining half of cucumber. Drain shredded cucumber on paper towels; press dry with paper towels and set aside.

Preheat oven to 400°. Spray a 15x10x1-inch baking pan with nonstick spray. Stir together lemon juice, 1½ teaspoon dill, salt, and black pepper into a small bowl. Add cherry tomatoes and red onions; toss to coat.

Remove chicken from bag; place in a single layer in prepared baking pan. Discard vinaigrette dressing. Scatter olives around chicken. Bake 14 to 16 minutes or until chicken reaches 165°.

Stir together tzatziki dressing, feta crumbles, and shredded cucumber in a small bowl.

To serve, coarsely chop olives; stir into tzatziki mixture. Spread hummus evenly onto pita bread; spread with tzatziki mixture. Top with romaine, chicken, tomato mixture, and cucumber ribbons. Fold in half. Garnish with additional dill, if desired.