If your chicken breasts are quite thick, slice them horizontally so they will cook quickly. Set aside in a glass dish.
Combine all marinade ingredients and pour over chicken breasts. Allow to marinate for 1 - 2 hours or up to 8 hours in the fridge.
Slice onion and peppers and chop tomatoes and set aside.
Prepare cauliflower rice (see 3 Easy Steps to Make Cauliflower Rice.)
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.