Preheat oven to 350°F (175°C) and lightly grease a 9x13 inch baking dish.
Cook chicken in boiling water until fully cooked (15-20 minutes), then shred into bite-sized pieces.
In a bowl, mix shredded chicken, garlic, cream of chicken soup, sour cream, green chiles, and half of the cheddar cheese.
Spoon mixture onto each tortilla, roll tightly, and place seam-side down in the baking dish.
Whisk remaining cream of chicken soup and chicken broth; pour over rolled enchiladas and top with remaining cheese.
Bake for 25-30 minutes until bubbly and golden brown.