Add butter to a 12-quart stockpot. Place over low heat and melt butter.
When butter has melted, gradually add 1 cup flour, stirring constantly with a wooden spoon. Cook, stirring constantly, 30 seconds.
Add 1 more cup flour and stir constantly 30 seconds.
Add remaining cup flour and stir constantly 30 seconds.
Continue to cook roux, stirring constantly, until it is the color of dark mahogany, about 45 minutes to 1 hour.
Add bell peppers and stir constantly 30 seconds.
Add onions and celery and stir constantly 30 seconds.
Gradually add stock to roux, stirring constantly with a wooden spoon to prevent lumps.
Add Andouille, Creole seasoning, salt, black pepper, red pepper flakes, chili powder, thyme, garlic and bay leaves. Stir to mix.
Increase heat and bring to a boil.
Reduce heat and simmer gumbo, uncovered, 45 minutes, skimming off any fat and stirring occasionally.
Add chicken meat and simmer 15 minutes.
Taste. Adjust seasoning with salt and hot sauce.
Serve steaming hot over prepared rice.