In a small bowl, whisk together all the peanut sauce ingredients. Add warm water one tablespoon at a time until the sauce reaches your desired consistency.
Heat avocado oil in a large skillet or wok over medium-high heat. Add chicken and sauté until browned and cooked through, about 6-8 minutes.
Add sliced bell peppers and shredded carrots to the skillet. Stir-fry for another 3-4 minutes until the vegetables are just tender.
Pour the peanut sauce over the chicken and vegetables. Stir to combine and heat through for 2-3 minutes.
Serve immediately over cooked rice. Garnish with green onions, crushed peanuts, cilantro, and lime wedges as desired.