Heat a saute pan, or any large heavy pan with a tight-fitting lid, on the stove over medium heat. Add the butter.
When the butter has melted, add the chopped onions, peppers and celery and cook, stirring occasionally, until softened (4-5 minutes).
Stir in the rice, and toast until lightly browned, stirring frequently so it doesn't burn. Slowly pour in the chicken broth, salt, and Cajun seasoning, and stir to combine.
Bring to a boil on the stove, then cover with a tight-fitting lid. If your lid is not tight-fitting, cover the pan first with a sheet of aluminum foil, and then with the lid, to prevent steam from escaping.
Bake 20-25 minutes until all the liquid is absorbed and the rice is tender. Remove from the oven and leave the lid on to let the rice steam another 5 minutes. Fluff with a fork and serve.