Combine the first six ingredients and set aside as a dipping sauce.
Prepare the other ingredients and set them out on your work surface. Set out a bowl of hot water and a clean kitchen towel.
Put a rice paper wrapper into the water for about 10 seconds, just until soft (don't let it become too soft; it will continue to soften as you work). Lay it on the towel.
In the middle of the wrapper, lay a quarter each of the chicken, carrot, lettuce, bean sprouts, scallions, cilantro, and peanuts (if using). Roll up, keeping it fairly tight and folding in the ends to seal. Repeat this process until all the ingredients are used up. Serve, with the dipping sauce.