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