Place a 6qt dutch oven over medium-high heat. Once the dutch oven is hot add 2 tablespoons of olive oil and heat it up until it starts sizzling.
Add the sliced sausage and sauté for about 5 minutes, stirring occasionally, until the sausage is nicely browned. Remove from pot and place on a plate, cover with foil to keep warm.
Add the cubed chicken and sauté for about 5-7 minutes or more, stirring occasionally, until the chicken is golden brown. Remove from pot and add it to the plate with the browned sausage, cover with foil to keep warm.
Add the remaining 2 tablespoons of olive oil and add the diced onion and garlic. Stir and cook for 1 minute.
Add chopped red and green bell peppers, diced celery, cajun seasoning, paprika, salt and black pepper. Stir and sauté for about 5 minutes, until the veggies are slightly softened.
Add the uncooked rice, stirring cook it for 1 minute.
Add the diced tomatoes, hot sauce (if using) and chicken broth, stir to combine. Add the chicken and sausage back to the dutch oven. Stir and cook until the mixture starts to simmer. Reduce heat to medium-low, cover the dutch oven with the lid and cook everything for about 15 minutes, stirring often, to make sure the rice does not burn or stick to the bottom of the pan.
After 15 minutes of cooking, add the raw shrimp to the dutch oven, stir and continue to cook for another 10 minutes, until the shrimp is cooked. If needed add more chicken broth, 1/3 cup at a time. Stir often, every 3-4 minutes now.
Taste the rice and adjust for salt, pepper and cajun seasoning if needed.
Remove from heat, garnish with fresh chopped parsley and serve.