Heat the oil in a 5 or 6 quarter Dutch oven or stock pot over medium until the oil shimmers.

Toss the chicken pieces with 1 teaspoon of Creole seasoning, and then add the chicken pieces in a single layer across the pot's bottom, and let heat for 1 to 2 minutes.

Flip the chicken pieces over to the raw side, and add the Andouille sausage to the pot.

Continue cooking, stirring occasionally, until the chicken pieces are cooked on the outside, and the sausage has begun to turn golden on the edges. (The chicken will finish cooking through when the soup and rice simmers.)

Scoot the meat mixture to the side to clear an area in the pot. Add the tomato paste, flour, and 1 tablespoon Creole seasoning to the cleared area. Stir together, and let the tomato paste cook for a minute or two and take on a little darkening. Stir everything in the pot together.

Add the onions, bell peppers, and celery to the pot and stir to mix well with the meat. Saute for 5 minutes. Stir in the garlic.

Add the crushed tomatoes, chicken broth, and rice. Bring the soup to an active simmer and cover with a tight-fitting lid. Cook for 15 to 20 minutes or until the rice is cooked.

Remove the lid and stir well; reduce heat to low.

Add the shrimp and cook in the residual heat of the soup until plump and opaque.

Taste the soup, and add salt to taste.