Have all your ingredients prepared. In a small bowl, stir chicken with sweet chili sauce. Fill a pie plate with warm water. Lay a damp smooth kitchen towel on the counter. Thinly cut peach halves into slices or use peach slices.
Working with 1 wrap at a time, dip in warm water until it is just pliable, 20 to 40 seconds. Place on kitchen towel. Place 1/2 a lettuce leaf near bottom of circle. Place 2 peach slices on top of lettuce, followed by 1/8 of chicken, then 1/8 of the cucumber and red pepper and 2 to 3 mint leaves depending on size.
Fold bottom (edge closest to you) of rice paper wrap over filling towards centre. Fold in sides to slightly cover filling. Then roll to totally enclose filling and form a roll. Set seam side down on a cutting board. Repeat with remaining ingredients. If sending for lunch, leave whole. If serving as an appetizer, slice in half diagonally. Serve with additional sweet chili sauce. Best eaten right away but if storing, make sure they aren't touching each other as they will stick. Cover with barely damp towel, then seal tightly with plastic wrap.