Place chicken in a pot, cover with water, and bring to a boil over high heat. Continue to boil until the chicken is done, about 10 minutes. Drain, allow chicken to cool, and cut into small pieces.
Place chicken pieces in a large bowl. Stir in soup, garlic, sour cream, and green chiles.
Spray the inside of slow cooker lightly with non-stick cooking spray.
Tear tortillas into pieces, and arrange half of the pieces in one overlapping layer across the bottom of the slow cooker. Arrange half of the chicken, half of the soup, and half of the cheese on top. Repeat with remaining tortillas, chicken, soup, and cheese. Top with black olives.
Cook on Low setting for 3 to 4 hours. Top with chives.