Place the noodles in a large heatproof bowl, pour over boiling hot water to cover and leave to stand for 10 minutes, or until just tender. Drain and return to the bowl. Add the chicken, cucumber, spring onions and chilli, and toss to combine. Transfer to a serving bowl.
Stir together the peanut butter, soy sauce, vinegar, honey, oils and 2 tablespoons of the measurement water in a bowl until well combined. Gradually add the remaining water to the sauce, stirring, until the sauce reaches pouring consistency.
Drizzle the sauce over the salad. Sprinkle over the sesame seeds and serve.