In a large skillet, heat butter over medium heat until melted. Stir in flour, cook for 1 minute and whisk in chicken broth. Continue stirring until smooth and thickened-- about 2-3 minutes.
Stir chipotle chili powder, salt, oregano and green chiles into the sauce and place chicken breasts into pan. Bring to a simmer, reduce heat to very low, cover and cook about 3 hours or until chicken is cooked through and shreds easily.
Remove chicken from pan, leaving the heat on low, and place chicken on a plate to shred into bite-sized pieces.
Stir sour cream into the sauce and return chicken to the pan. Stir until combined and top with grated cheese. Cover pan and cook for 5-8 minutes until bubbly and the cheese is melted.
