Cook the noodles according to package directions. Drain and set aside.
Whisk together peanut butter, soy sauce, honey, rice vinegar, sriracha, sesame oil, and warm water until smooth. Set aside.
Heat oil in a large skillet or wok over medium-high. Add chicken and cook until just golden and cooked through, about 5-6 minutes.
Toss in bell pepper and snap peas. Stir-fry for 2-3 minutes until crisp-tender.
Add cooked noodles, peanut sauce, and green onions to the pan. Toss well to coat.
Top with chopped peanuts, fresh cilantro, and lime wedges.