You'll need a glass baking dish large enough to hold 6 enchiladas. Preheat oven to 350°F.
Trim off any excess fat or skin off of chicken breasts. Wash thoroughly and place chicken in a deep pan with chicken broth and water. Add salt and pepper. Bring to a boil, then down to a simmer. Cover with lid and let cook till chicken is easy to shred with fork.
Discard broth. Shred chicken with fork and set aside. Combine all cheeses and onion in a small bowl.
Open small can of green chile sauce and pour on bottom of glass baking dish. Fill each tortilla with shredded chicken, diced green chiles, cheeses, onion, and top with 1 tbsp. of green chile sauce. Reserve half the cheese and onion combination.
Roll tortillas and place in baking dish seam side down. Take remaining green chile sauce and thoroughly pour over all. Top with remaining cheeses, onion, the salsa Veda and black olives. Bake in 350°F oven for 20 to 25 minutes or until heated through and cheese has melted. Let stand 5 minutes. Top with sour cream or your favorite hot sauce.
