Preheat broiler to high.
Combine chili powder, salt, and pepper in a small bowl. Put sliced peppers and onions on a foil-lined rimmed baking sheet. Drizzle veggies with 1 tablespoon of olive oil and season with half of the seasoning mixture.
Broil for 10 minutes on the top rack until softened and starting to char.
Meanwhile, slice chicken into 1/4-inch-thick strips. In a large bowl, toss chicken with remaining seasoning mixture and 1 tablespoon of olive oil.
When the veggies are ready, place chicken strips over veggies. Return the sheet to the top rack of the broiler and cook for another 5 minutes. Chicken should be cooked through and starting to brown. Do not overcook.
Squeeze a lime over the chicken. Serve with tortillas and favorite fixings.