In a large skillet or wok, heat the vegetable oil over medium-high heat. Add the chicken pieces and stir-fry until golden brown and fully cooked, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the sliced onion, bell pepper, garlic, and ginger. Sauté for 2-3 minutes until the vegetables are slightly tender.
Add the broccoli, carrot, and snap peas to the skillet. Continue to stir-fry for another 3-4 minutes until the vegetables are vibrant and crisp-tender.
While the vegetables are cooking, prepare the peanut sauce. In a bowl, whisk together the peanut butter, soy sauce, honey, lime juice, and chili paste until smooth.
Return the cooked chicken to the skillet and pour the peanut sauce over the chicken and vegetables. Stir everything together until well coated and heated through, about 2-3 minutes.
Taste and adjust seasoning if needed, adding more soy sauce or chili paste for spice.
Serve your Thai peanut chicken hot, garnished with fresh cilantro and chopped peanuts.