Sauce: In a medium bowl, stir together vinegar, honey, dressing, and red pepper. Set aside.
Chicken: In a large skillet, heat oil over medium heat, add chicken, cover and let simmer. Flip chicken after about 5 minutes, cover, and let simmer 5 more minutes.
Pour sauce over chicken and stir. Then, add asparagus, carrots, and red pepper to the skillet. Turn heat to low, cover, and let simmer until the veggies are cooked.