3 Tablespoons Butter
3 Tablespoons All-Purpose Flour
2 Cups Chicken Broth
1 (4 Ounce) Can Chopped Green Chilies
1 (4 Ounce) Can Sliced Black Olives
1/2 Teaspoon Kosher Salt
1/4 Teaspoon Dried Oregano
1/8 Teaspoon Chipotle Chile Powder
4 Skinless, Boneless Chicken Breast Halves
1 Cup Sour Cream
12 (6 Inch) Corn Tortillas, Cut Into Bite-Size Pieces
2 Cups Shredded Colby-Jack Cheese, Or To Taste
1 Cup Cheddar
Melt butter in a large skillet over medium heat. Stir in flour; cook for 1 minute. Whisk in chicken broth; cook and stir until sauce is smooth and thickened, 2 to 3 minutes.
Stir green chiles, olives, salt, oregano, and chipotle chile powder into the sauce. Add chicken breasts and bring to a simmer. Reduce heat to low, cover, and cook until chicken is no longer pink in the center and the juices run clear, about 15 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Remove chicken from the skillet, leaving heat on low. Place chicken on a plate; shred into bite-size pieces.
Stir sour cream into the sauce. Return chicken to the skillet; add tortilla pieces. Stir until combined and top with Colby-Jack cheese. Cover and cook until bubbly and melted, 5 to 8 minutes.