Place a large, heavy soup pot or Dutch oven over medium-high heat and add the oil. Add the sausage, onion, and celery, and cook, stirring frequently, until the onion is softened and slightly golden and the sausage no longer pink, about 15 minutes.
Add the black-eyed peas, broth, tomatoes, chiles, and chili powder. Stir to blend and add the salt and pepper to taste.
Bring to a boil, then reduce the heat to low, cover, and simmer for about 45 minutes. Taste for seasoning.