In large pan over medium high heat, bring water to boil. Add chicken breast, and return to boil. Reduce heat to low. Simmer, uncovered, about 15 minutes. Remove meat and set aside to cool.
Bring stock water to boil again, and add noodles. Cook, stirring occasionally, 5 to 7 minutes. Drain, reserving stock for another use if desired. Rinse pasta under cold running water until chilled. Drain again, and transfer to serving bowl. Toss lightly with 1 teaspoon sesame oil.
Cut or pull chicken meat into fine shreds, discarding skin and bones. Set aside.
Combine tahini and 3 tablespoons water, stirring to blend. Add chilli oil, soy sauce, vinegar, 1 tablespoon sesame oil, groundnut oil and garlic. Mix well.
Arrange the chicken on top of noodles in serving dish. Spoon sauce over all.