Heat the vegetable oil in a large pot or Dutch oven over medium-high heat. Add the sliced sausage and cook until browned, about 5 minutes. Remove the sausage and set aside.
In the same pot, add the chopped onion, bell pepper, celery, and minced garlic. Sauté until the vegetables are soft, about 5-7 minutes.
Stir in the chicken thighs and cook until browned on all sides, about 5 minutes.
Return the sausage to the pot and add the chicken broth, diced tomatoes (with juices), Worcestershire sauce, Cajun seasoning, thyme, and cayenne pepper. Stir to combine.
Bring the mixture to a simmer, then reduce the heat to low. Cover and cook for about 45 minutes, stirring occasionally.
After 45 minutes, add the sliced okra to the pot and stir. Cook for another 15-20 minutes, uncovered, until the gumbo has thickened and the chicken is tender.
Remove the chicken thighs from the pot, shred the meat, and return it to the gumbo. Season with salt and pepper to taste.
Serve hot over cooked white rice and garnish with fresh parsley.