Fully cook the chicken breasts, and cut into 16 strips.
Cut and wash full leaves of romaine; remove the leaves.
Peel cucumber and slice into strips lengthwise.
Shred the carrots.
Combine 2 tbsp rice vinegar with 2 tbsp sugar.
Divide sweetened rice vinegar in half, adding half to cucumber and half to shredded carrot; set aside.
Cook the rice noodles in boiling salted water for 3-4 minutes; drain. Immediately rinse with cold water and drain again.
Fill a flat dish with warm water and place rice sheet in water for 15-30 seconds. Lay on dry towel to remove excess water.
On flat plate or cutting board, place wet rice paper flat (this part is tricky). Without over stuffing—(to avoid ripping the rice sheet)—place romaine leaf, chicken, cucumber, rice noodle, cilantro, and carrots side by side on sheet. Carefully roll ingredients into the paper, making sure to tuck in the sides.
Serve with peanut or sweet chile sauce.