Heat olive oil in a large cast iron pot over medium-high heat. Add the chicken pieces and minced garlic. Sauté until chicken thighs are browned (5 minutes).
Stir in the onion, bell pepper, and celery and cook for 5 minutes until vegetables are softened.
Add the salt, cajun seasoning, cayenne, and cook for 2 minutes.
After adding the crushed tomatoes and beef broth reduce heat to medium and cook for 5 minutes, add the Andouille sausage and butter. Turn the heat to medium-low and simmer for 20 minutes. During the last 2 minutes add Gumbo filé.
Add the shrimp and cook for 3 minutes. Serve hot with a side of hot sauce for those who want more heat.
You can substitute Kielbasa for Andouille sausage. If you feel there is too much heat eliminate the cayenne pepper. Simmering the gumbo longer will intensify the flavor and thicken the stew. We usually add the Gumbo filé early in the process, but some feel it is better for taste and thickening to add the filé at the end. We have tried it both ways and see little difference in taste. Some even add the filé after serving for taste. Keep some on the table.