Heat oil in skillet until it shimmers. Carefully add chicken breasts and sear. Cook on each side for about 5-7 minutes (if thinly sliced, longer if thicker) until meat thermometer registers at least 165°F and juices run clear. Remove from pan, cover with foil and let rest. while you quickly sauté the peppers and onions.
Assemble the bowls with the cauliflower rice, peppers, onions and tomatoes.
Peel and slice avocado last to prevent browning. Add chicken to dish, drizzle with pan juices and serve immediately.