Heat oil in a large pot or Dutch oven over medium-high heat. Season chicken with salt and pepper. Sear chicken until browned on all sides. Remove chicken and set aside.
Add sausage to the pot and cook until browned. Remove sausage and set aside.
Add onion, bell pepper, and celery to the pot and cook until softened, about 5-7 minutes. Add garlic and cook for 1 minute more.
Stir in flour and cook for 1-2 minutes, creating a roux.
Gradually whisk in chicken broth, scraping up any browned bits from the bottom of the pot.
Add bay leaves, thyme, cayenne pepper, salt, and pepper. Bring to a boil, then reduce heat and simmer for 30 minutes.
Return chicken and sausage to the pot. Simmer for another 30 minutes, or until chicken is cooked through.
Remove chicken and shred the meat. Return the shredded chicken to the pot.
Stir in file powder. Serve hot over cooked rice.