Heat the oil on medium in a large Dutch oven on the stove top.
Add onion, celery, and bell pepper and cook about 5 minutes.
Add garlic, basil, oregano, and thyme and stir. Cook for about 5 more minutes.
Add the chicken and sausage and let brown for 5-10 minutes, stirring often.
Add cayenne pepper and paprika to the meat mixture and blend lightly.
Pour in the crushed tomatoes, chicken broth, and rice and mix. Bring to a light boil, then lower the heat to 1-2 and cover.
Cook covered on low for 45 minutes, stirring a couple times to make sure the rice isn't sticking to the bottom.
During the last 5-10 minutes of cooking, add the shrimp to the top of the mixture and cover. Check again after about 5 minutes and flip shrimp over, making sure not to cover it deeply so you can keep an eye on its doneness. Cover and cook 5 more minutes or until shrimp is opaque pink and white.
Serve right away with a side salad and crusty bread if desired.