Combine the oregano, cumin, chili powder, cayenne pepper, salt and black pepper in a small bowl. Drizzle a little olive oil on the chicken pieces and rub the spice mixture on all sides of the chicken.
Warm the tortillas by either popping them into a 350ºF oven wrapped in foil for about 10 minutes, or by frying each one in a little olive oil over medium-high heat for about 1 minute per side. Set up all your favorite toppings and let everyone build their own taco.