Cook the chow mein noodles according to package instructions. Drain and set aside.
In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the diced chicken and season with salt and pepper. Cook until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the red and green bell peppers, snap peas, green onions, garlic, and ginger. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
In a small bowl, whisk together the soy sauce, rice vinegar, hoisin sauce, cornstarch, and water. Pour this sauce over the vegetables in the skillet and stir to combine.
Return the cooked chicken to the skillet and add the chow mein noodles. Toss everything together until well coated in the sauce and heated through, about 2-3 minutes.
Drizzle with sesame oil and sprinkle with roasted peanuts before serving.