In a medium size bowl whisk together the peanut butter, soy sauce, fish sauce, rice vinegar, 2 tablespoons sesame oil, ginger, garlic, brown sugar and chili sauce.
In a separate bowl, add the chicken and toss with 2 tablespoons of the peanut sauce mixture. Let marinate at least 10 minutes and up to a day. Heat a grill, grill pan or heavy frying pan over medium-high heat. Cook the chicken until browned and just done, 3-4 minutes per side. Remove the chicken from the pan and let it rest for 5 minutes.
Cook the noodles in large pot of salted boiling water to al dente, according to package instructions. Reserve 1 cup of the cooking liquid, then drain well and transfer to a large serving bowl. Toss with the remaining 2 tablespoons sesame oil until evenly coated. Pour the remaining sauce over the noodles and mix well until fully combined. If it's too thick, thin it with a few tablespoons of the reserved noodle cooking water. Add the scallions and grilled chicken and toss again.