In a large pot, heat vegetable oil over medium heat.
Add flour and stir to create a roux, cooking until golden brown.
Stir in onions, bell pepper, and celery; sauté until softened.
Add garlic and cook for an additional minute.
Incorporate the sliced sausage and cook until browned.
Add the chicken thighs, cooking until browned on all sides.
Pour in diced tomatoes and chicken broth, stirring well.
Season with Cajun seasoning, salt, and pepper.
Bring to a boil, then reduce heat and simmer for 30 minutes.
Serve over cooked rice and enjoy!