In a large skillet, heat the vegetable oil over medium-high heat. Add the chicken pieces and 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 bell pepper, snap peas, and carrot. Sauté for 3-4 minutes until the vegetables are tender-crisp.

While the vegetables are cooking, in a small bowl, whisk together the peanut butter, soy sauce, honey, rice vinegar, lime juice, garlic, ginger, and red pepper flakes until smooth.

Return the cooked chicken to the skillet with the vegetables. Pour the peanut sauce over the mixture and stir to combine. Cook for an additional 2-3 minutes until everything is heated through.

Serve the chicken and vegetable mixture over a bed of brown rice. Garnish with chopped green onions and cilantro, and serve with lime wedges on the side.