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Preheat grill to medium-high (if grilling chiles) or preheat oven to 400°F (if roasting chiles).
Place chicken and broth in a large saucepan; bring to a boil. Cover, reduce heat to a simmer and cook, turning the chicken halfway through, until no longer pink in the middle, 10 to 15 minutes, depending on size. Remove from the heat. Transfer the chicken to a clean cutting board, leaving the broth in the pan. When cool enough to handle, shred or chop the chicken into bite-size pieces.
Meanwhile, grill chiles, turning frequently, until blistered on all sides, about 15 minutes. (Alternatively, roast on a baking sheet, turning once or twice with tongs, until blackened in places, 15 to 20 minutes.) When cool enough to handle, peel and remove stems and seeds. Finely chop 2 chiles; puree the other 2 in a food processor or blender with 1/4 cup of the hot broth.
Whisk 1/2 cup of the broth in a bowl with wine and flour until smooth. Return the pan with the broth to medium heat and whisk in the flour mixture until well combined. Stir in the chopped and pureed chiles and the chicken. Add milk, salt, white pepper and oregano; heat, stirring frequently, until steaming and hot, but not boiling, 10 to 15 minutes. Remove from the heat and stir in cilantro.