1. Cut chicken breasts so that center thickness is around 1/2-inch to 3/4-inch thick. Mix all marinade ingredients together and add to chicken. Cover and let marinate at room temperature for 1 hour. (Can marinate in fridge for up to 8 hours, but remove an hour before cooking to allow to come room temp.)
2. Remove chicken from marinade, and sprinkle chicken pieces with salt. Heat large pan with 1 tablespoon oil. Add chicken and cook each side of 2-3 minutes for a good sear. Remove from pan and let rest for 5 minutes.
3. Using same pan, add 1 tablespoon of oil. On high heat, cook onions and peppers to pan. Use spatula to stir and coat vegetables in flavor from the pan. Spread onions and peppers in even layer in pan. Let cook undisturbed for 2 minutes to sear with some blackening. Stir vegetables and continue to cook for another 2 minutes.
4. Slice chicken into strips. Serve at once with the peppers and onions, warm tortillas, and sides of shredded cheese, salsa, guacamole, and/or thinly sliced iceberg lettuce dressed with vinegar and salt.