A good Cajun chicken gumbo typically starts with a dark roux and flavorful ingredients, such as sausage or ham, and Cajun spices. Many utilize the classic Cajun aromatic vegetable combination known as the holy trinity, which includes onion, celery and bell pepper.
Cook 1 pound of sausage or 3/4 pound of diced ham in a heavy-bottomed pot over medium heat until it's browned. Transfer the meat to paper towels, and brown four chicken breasts. Set the chicken aside and add 1/2 cup vegetable or olive oil to the pot. Heat the oil mixture over medium heat, and add 3/4 cup of all-purpose flour. Stir it constantly, and cook the flour and oil for approximately 20 minutes until it looks similar to chocolate.
Add 1 chopped onion, two sliced ribs of celery and half a green bell pepper with the roux until the vegetables are tender. Add 2 quarts of liquid, and bring it to a boil. Add three or four minced cloves of garlic, two bay leaves, 1 teaspoon of hot sauce and 2 teaspoons of Creole seasoning. Simmer the mixture for one hour, stirring it occasionally. Slice the chicken into chunks. Add the chicken and sausage back to the pot along with sliced green onions, and simmer it for another 20 to 30 minutes. Serve the chicken gumbo over hot rice.