For the chili: Sprinkle the chicken with 1/2 teaspoon salt and several grinds of black pepper. Heat the oil in a large Dutch oven over medium-high heat. Add the chicken and cook, stirring occasionally, until brown all over, about 6 minutes. Reduce the heat to medium, add the garlic, celery and onion and cook, stirring occasionally, until the vegetables are just softened, about 4 minutes. Stir in the chili powder and cumin to coat the chicken and vegetables. Add the broth, beans, tomatoes, tomato sauce and desired amount of hot sauce. Bring to a simmer, cover and cook until the chicken is tender, 30 to 40 minutes.
For the toppings: Stir together the mayonnaise, sour cream, vinegar, garlic powder and 1 tablespoon water in a small bowl. Stir in the blue cheese and scallion whites. Season with salt and pepper.
To serve, spoon rice into servings bowls and top with the chili. Add a dollop of the blue cheese dressing and a sprinkle of scallion greens. Serve with the celery and carrot sticks and additional hot sauce.