Clean the alligator meat and cut it into bite-sized pieces. Toss with one tablespoon of flour, salt, and pepper to lightly coat.
In a large pot or Dutch oven, heat the olive oil over medium-high heat. Sear the alligator meat on all sides until golden brown. Set aside.
Chop the onion, garlic, bell peppers, and celery. In the same pot, sauté these vegetables until softened.
Add the remaining tablespoon of flour to the vegetables and cook for 1-2 minutes, allowing the flour to lightly brown.
Pour in the chicken stock, then add the diced tomatoes, Cajun seasoning, and bay leaf. Stir well to combine.
Return the alligator meat to the pot and reduce the heat to low. Cover and simmer for 1-1.5 hours, or until the meat is very tender.
Once cooked, remove the bay leaf. Taste and adjust seasoning with additional salt and pepper, if needed.
Serve the stew hot with fresh crusty bread or cooked rice to soak up the rich sauce.
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