Bake bread according to package directions, then cool. Cut loaf horizontally.
Combine ground chicken, cherries, cherry peppers, rosemary, and salt and pepper in large bowl. Stir well to combine. Shape into 4 patties. Mist a large nonstick fry pan with cooking spray. Place over medium heat until hot. Cook burgers for about 5 minutes per side, or until cooked through.
Stir preserves into mayonnaise in small bowl. Spread on cut sides of bread. Cut the loaf into 4 equal sections. Top the bottom bun with burger then tomato slices and 2 pieces lettuce. Place top bun on lettuce.