In large pot; add broth to cover. Over high heat, bring to a boil; reduce heat and simmer, covered, about 20 minutes or until chicken is cooked through.
Cool chicken in broth. Remove chicken from broth; strain and reserve broth. Remove and discard skin and shred chicken into bite-size pieces.
In saucepan over medium heat, heat oil with garlic and ginger just until it sizzles.
Remove from heat; whisk in tahini, chili sauce, soy sauce, vinegar and sugar. Slowly whisk in broth until sauce has a thin, creamy consistency.
Soak noodles in hot water about 5 minutes or until soft; drain. Cook noodles in boiling water about 3 minutes or until transparent; drain and cool in cold water. Drain well; toss with oil.
Place 3/4 cup noodles in center of bowl or plate. Toss 1/2 cup chicken with 2 tablespoons sauce; mound on top of noodles. Arrange 1/4 cup cucumbers on one side of noodles and 1/4 cup green onions on opposite side. Sprinkle plate with 1 teaspoon sesame seed.