Preheat a gas or charcoal grill over high to medium-high heat. Preheat a grill basket on the grill for at least 5 minutes before adding the veggies.
Toss the peppers and onions with 1 to 1-1/2 tablespoons of fajita seasoning and a drizzle of oil.
Rub another 1 to 1-1/2 tablespoon of fajita seasoning into the chicken breasts so they are evenly coated.
Put the chicken on the grill and the veggies in the grill basket. Cook the chicken for 8-10 minutes, flipping once. Remove from grill and rest for 3-4 minutes before slicing. Stir the veggies periodically and cook until they begin to soften (or to your preference) and develop a bit of a char.
Serve the veggies and sliced chicken with warm flour tortillas, cheese, sour cream, lettuce and tomato.