In a large Dutch oven set over medium heat, melt the butter. Gradually whisk in the flour, continuing to whisk constantly to prevent the mixture from burning. Cook for 15-20 minutes until the roux reaches a light chocolate brown color, indicating it is ready for the next step.
Due to the roux's heat and potential splatter, stir in the onion, green pepper, and celery carefully. Cook for 4-5 minutes, or until the vegetables begin to soften, stirring often. Then, add the sausage and minced garlic, cooking for an additional 1-2 minutes.
Add the chicken broth, creole seasoning, smoked paprika, salt, pepper, and cayenne pepper and stir.
Add the chicken to the pot and increase the heat to bring the mixture to a boil. Then, lower the heat to a gentle simmer, letting it cook for 60-80 minutes. You'll want to see the gumbo thicken before moving on to the next step.
Remove the chicken breasts, and shred them into bite size pieces with 2 forks.
Return the chicken to the pot and stir. Serve immediately with cooked white rice and sliced green onions.