Cut the chicken into 1-inch bite-size pieces. Chop all the vegetables.
Place the butter in a large skillet or sauté pan, with a lid. Set over medium heat. Add the chopped onions and celery. Sauté for 3-5 minutes to soften.
Add the chicken pieces, rice, hot sauce, broth, and 1/4 teaspoon salt. Stir, then cover the skillet. Bring to a boil. Lower the heat and simmer for 15 minutes, or until the broth has absorbed and there are air vent holes in the top of the rice.
Fluff the rice with a fork. Stir in the cheddar, blue cheese, and green onions. Taste, then salt and pepper as needed.