Lay out the fillings on a large platter or cookie sheet for easy access. (Cut carrots and cucumbers into thin sticks.)
In a small mixing bowl, whisk together sauce ingredients, and set aside.
Fill a wide, shallow dish (or a plate with a lip) with lukewarm water.
Place a rice paper wrapper in the dish for about 20 seconds to allow it to begin to soften and saturate.
Move the wrapper to a clean plate and place a small amount of chicken, cucumber, carrrot, and cilantro inside.
Carefully fold the edges of the wrapper in and roll it up, snugly but gently. Set aside.
Repeat steps 4-6 with remaining wrappers. Eat cold, dipped in peanut sauce.