Add all marinade ingredients to the jar of a food processor. Pulse until thoroughly blended. If it gets stuck, you can drizzle in more olive oil a little bit at a time until it moves along enough to blend well. The marinade should be pretty thick, not runny.
Add the marinade and chicken breasts to a gallon size zip bag. Press out excess air and zip the bag shut. Squish the contents around so the marinade covers all the chicken. Pop in the fridge and allow to marinate 5 hours or overnight.
Cook the chicken as desired--on a grill, in a smoker, in a skillet, in the oven, etc. until the internal temperature reads 165° F.
Allow chicken to rest for 10 minutes then cut into ½-inch chunks or strips.
Serve in tortillas with toppings and add-ins of choice such as shredded cheese, tomatoes, cauliflower rice (or real rice for an XO), olives, lettuce, sour cream, and so on.