Heat the broiler with one rack positioned about 4 inches away.
In a small bowl, whisk together the first seven ingredients. Set aside 1/4 cup of the sauce, then place the rest, along with the chicken, in a large ziplock bag. Seal the bag and turn it to coat the chicken.
Toss the peppers and onion with the reserved marinade on a rimmed baking sheet. Spread them out evenly. Place the marinated chicken on top.
Broil, turning the chicken halfway through, until the chicken is no longer pink inside and the vegetables are charred, about 12 minutes. Slice the chicken into strips before serving with your favorite fajita toppings.