Drizzle chicken breasts with a little soy sauce and place in a bamboo steamer. In a saucepan add 200 ml (approximately 6 3/4 ounces) of water with rice vinegar, bring to a boil, cover the bamboo insert and steam for 8-10 minutes. Remove, let cool and cut into strips.
Rinse or peel celery, carrots and bell pepper and cut into thin sticks. Rinse lettuce leaves, pat dry and pluck small as needed. Rinse basil and pluck leaves.
Fill a shallow dish with water, slightly larger than the sheets of rice paper. In addition, spread a cloth and have a second cloth handy. Place sheets one at a time into the water and soak for about 1 minute. Then gently spread on the cloth and pat dry with a second cloth.
Into the center of each rice sheet, place some salad, Thai basil, prepared vegetables and chicken. Drizzle with a little soy sauce. Fold the sides of rice paper inward and roll up tightly.
Halve the rice paper rolls for serving in the middle once diagonally and serve with dips as desired.