Take a stock pot or Dutch oven and heat the vegetable oil in it on medium flame. Add the sausage and cook for five minutes or until it has turned brown.
Remove the sausage from the pot and add boneless chicken thighs to it, cook it for seven minutes while stirring constantly. After the chicken has been cooked, remove it from the pot and place it aside.
Add the flour to the pot while stirring continuously, for 10-15 minutes, till dark roux forms.
Add all the vegetables to the pot. Cook for 10 minutes until the vegetables become tender.
Gradually pour the chicken broth into the pot, stirring often. Now add the thyme, hot sauce, bay leaves, and Cajun seasoning to the pot, stirring constantly to combine thoroughly.
Bring the stew to a boil while stirring in the cooked chicken and sausage. Simmer for around 30 minutes on a low flame.
Add shrimp to the pot and cook for a further 5 minutes until the shrimp is fully cooked and pink in color.
Take the bay leaves out of the pot and discard them. Add the salt and pepper as per your preference.
Serve it with cooked white rice.