1.Cook noodles according to package instructions. Drain, then run under cold water until cool. Drain, cover and set aside.
2.Bring some water in a pot to a boil, add chicken. Cover, turn off heat, steep for 15 minutes. Remove meat, let cool. Tear along grain into thin strips.
3.Make dressing: Add sesame paste to a mixing bowl with peanut butter. Add a 1/3 of water, stir.
4.Add garlic, sugar, salt, and another 1/3 of water, stir.
5.Add soy sauce, vinegar and remaining water, stir.
6.Place noodles in large individual bowls. Put cucumber, carrots, and chicken on top of noodles.
7.Stir dressing again, and spoon equal portions onto noodles.
8.Diners should mix ingredients together before eating.