Boil chicken in chicken broth (canned or bouillon) until meat is falling off bones. Allow to cool in the broth. Remove skin and bones from chicken. Dice chicken (if desired, strain broth and keep for a great base for soup or to cook chicken in next time).
Mix diced chicken with salsa, cheese, green chiles, and olives. Cover half of a tortilla with chicken mixture and fold other half over top. For soft quesadillas, heat in microwave. For crisper ones, bake on cookie sheet a few minutes at 350 degrees. For very crisp ones, fry in hot oil. Cut into 3 wedges and serve with dip, if desired.
