Fry poblano peppers in grease until skin bubbles. Cool, peel off all skin. Cut open, remove stem and all seeds. Cut peppers into strips.
Cut chicken into strips and cook in large skillet. Drain off all liquid/grease. Add peppers, butter, and milk to chicken. Cook on medium heat until starts to boil, turn off burner. Add cheese and cover about 5 minutes or until cheese melts.
Heat flour tortillas in microwave. Serve mix in tortillas.