Cut chicken into 1/4–inch thick slices that are 4 to 5 inches long. Mix soy sauce and lime juice into a marinade in a small bowl and pour over chicken. Cover chicken with plastic wrap and marinate for at least 15 minutes but up to several hours. Discard leftover marinade. Sauté peppers and onions in hot oil in a large skillet over high heat for 2 to 3 minutes. Pour teriyaki sauce evenly over vegetables; toss to combine. Remove from heat, cover and serve with chicken and tortillas.
Set grill grids at low position. Preheat grill to high. Heat tortillas on grill warming rack until warm then stack tortillas and wrap in aluminum foil to hold in heat. Grill chicken about 3 to 5 minutes on each side until 180°F internal temperature is achieved. To assemble fajitas, place 2–3 strips of grilled chicken onto tortilla, add peppers, onions, shredded cheese, sour cream, and avocado (optional). Wrap and enjoy.