In a medium saucepan, heat the oil over medium heat. Add the chicken and stir frequently until cooked through, about 15 minutes.
Add 2 cups white beans, the poblanos, onion and garlic. Cook, stirring frequently, until the beans break apart, about 15 minutes.
Stir in the chicken broth, cumin, oregano and chipotle powder, then lower the heat to low. Add the remaining beans and 1 cup jack cheese; stir just until melted, about 5 minutes.
In a dry skillet or a warm oven, heat the tortillas. Fold the tortillas into quarters.
Top portions of the chili with 2 tablespoons cheese, 1 tablespoon sour cream, a cilantro sprig and a folded tortilla.