Drizzle the chicken with some oil, season with salt and pepper and put on a baking sheet. Roast until the internal temperature registers 165 degrees F on a meat thermometer, 15 to 20 minutes. Set aside until cool enough to handle, then cut into large dice.
Meanwhile, add 1/4 cup oil to a large Dutch oven and heat over medium heat. When hot, add the celery, onions and bell peppers and saute until tender, 4 to 5 minutes. Add the flour, stir to coat the vegetables and cook until the flour starts to brown, about 3 minutes. Whisk in the warm chicken stock, stirring until combined. Add the beans, chiles, garlic powder, cumin, rosemary and green tomatoes and bring to a simmer, cooking until the mixture starts to thicken, 15 to 20 minutes.
Add the diced chicken and cayenne and season with salt and pepper. Cover and cook for another 10 minutes to warm through. Serve garnished with sour cream.