Put the chicken in a large pan of water. Bring to a boil and
simmer for 20 minutes, skimming off the scum from time to time.
The poaching water can be put toward making stock. When the
chicken is cooled, shred with your fingers or with a knife.
Slice the cucumber slices into matchsticks.
Mix the peanut butter, sugar, vinegar, chicken stock, soy sauce,
sesame oil and chile oil together in a bowl.
Bring a large pan of water to a boil, and add the noodles. Cook
for 3 minutes, rinse, and drain. Toss the noodles in the sesame
oil, then arrange them on individual plates.
Place a quarter of the shredded chicken and cucumber onto each
serving of noodles. Pour on the peanut sauce and serve
immediately.