Pat chicken strips dry with paper towels and set aside.
In a medium bowl, whisk together peanut butter, soy sauce, honey, rice vinegar, ginger, garlic, lime juice, and red pepper flakes if using. Add 2 tablespoons water to create a smooth, pourable sauce.
Heat vegetable oil in a wok or large skillet over high heat until shimmering.
Add chicken strips in a single layer (working in batches if necessary) and cook undisturbed for 1-2 minutes, then stir-fry until cooked through, about 3-4 minutes total.
Add bell pepper, snap peas, carrots, and water chestnuts (if using) to the wok. Stir-fry for 2-3 minutes until vegetables are bright and crisp-tender.
Reduce heat to medium-low and pour the peanut sauce over the chicken and vegetables. Toss gently to coat everything evenly.
Cook for 1-2 minutes until sauce thickens slightly and becomes glossy. If too thick, add 1-2 tablespoons of water.
Drizzle with sesame oil if using, toss once more, then remove from heat immediately.
Transfer to a serving dish and garnish generously with sliced green onions, sesame seeds, chopped peanuts, and cilantro if using.
Serve immediately over steamed rice or noodles.
Notes
For extra-tender chicken, try the velveting technique: toss sliced chicken with 1 tablespoon cornstarch, 1 teaspoon baking soda, and 1 tablespoon oil. Let rest for 15 minutes before cooking.
This dish keeps well in the refrigerator for up to 4 days. Store sauce-coated chicken and vegetables separately from any rice or noodles.
For a spicier version, add 1-2 tablespoons of chili garlic sauce to the peanut sauce mixture.
Nutrition facts are estimates and may vary based on ingredients used, portion sizes, and preparation methods.