Bring a large saucepan of water to the boil and cook the noodles for 2 minutes. Refresh in cold water, drain and transfer to a large salad bowl.
Add the cabbage, carrot, cucumber and lime juice to the noodles.
Gently warm the peanut butter in a small saucepan. Add the sweet chilli sauce, soy sauce, vinegar and sesame and vegetable oils and whisk to a pouring consistency. (If necessary, add a little warm water to achieve the correct consistency.) Set the sauce aside to cool slightly.
Shred the chicken breasts, add the meat to the noodle mix and combine well. Arrange on serving plates, spoon over the peanut sauce and garnish with finely sliced spring onions.