Fill a large saucepan two-thirds full of water and bring to a boil over high heat. Salt it so that it tastes good, add the chicken breast, and remove the pot from the heat. Cover and let the chicken sit until cooked but very tender, about 15 minutes. Remove the chicken from the water and cut into it to check its doneness; if it's still a little pink, return it to the water for another minute or two. Remove the chicken to a plate and let it rest.
Place a large skillet over medium-high heat and once the pan is heated, add in the zucchini noodles and cook for 5 minutes or until al dente.
Meanwhile, in a medium bowl, whisk together the sesame oil, peanut oil, tahini, soy sauce, vinegar, chili oil, honey, cayenne, and garlic until smooth.
Shred the chicken with your hands or chop it into bite-size pieces and add it ot the noodles. Add the dressing and toss to coat. Garnish with the scallions.