In a large pot or Dutch oven, melt butter over medium heat. Add onions, bell pepper, and celery and cook until softened, about 5-7 minutes.
Stir in flour and cook for 1-2 minutes, creating a roux.
Gradually whisk in chicken broth until smooth. Bring to a simmer.
Add cayenne pepper, thyme, oregano, salt, and pepper. Simmer for 15-20 minutes, stirring occasionally.
Add chicken thighs and alligator (if using) to the pot. Bring to a simmer and cook until chicken is cooked through, about 20-25 minutes.
Add okra and tomatoes. Simmer for another 10-15 minutes.
Stir in green onions before serving.