Combine all the marinade ingredients in a bowl and whisk together. Add the chicken and marinade for 12-24 hours (overnight) for best results.
Heat a grill to 400F. Grill the chicken for 4-6 minutes on each side. The internal temperature of the chicken should be 160F when removed from the grill. It will rise to 165F as it rests.
Once the chicken has rested for 5-10 minutes, slice it into strips.
Get a large bowl of warm water and dip a piece of rice paper in for about 10 seconds.
Place on a plate and let it sit for 20-30 seconds to become pliable.
Add the carrots, cucumber,bean threads, green onions, mint, basil and chicken strips.
Fold the side edges up and roll it up like a burrito (see photos in post above). You can leave the ends open if it's easier.
Peanut Dipping Sauce:
Place all ingredients in a blender and pulse until smooth.
Be sure to let the chicken marinade for at least 12 hours for maximum flavor.
You can also broil the chicken in the oven if you don't have a grill. Place it about 6" from the broiler and cook for 4-6 minutes per side, until internal temp reaches 160F. Be sure to watch the chicken and make sure it doesn't burn (different broilers will act differently).
Make sure your chicken and vegetables are sliced and ready to go before wetting the rice paper. The rice paper can be sticky to work with, it helps if your fingers are a little wet.
Make the chicken and peanut sauce ahead of time to save time if desired (perfect for "make your own" food parties).