Heat the olive oil and butter in a nonstick pan over medium. Add the chicken and cajun seasoning and cook for a couple minutes on each side, or just until the outside gets some color.

Add the onion, peppers, celery, and garlic to the pan and sauté for about 2 minutes more, or just until the onion begins to soften. Stir in the flour and cook for 1 minute.

Next, add the diced tomatoes and chicken broth. Stir until everything is evenly combined, then place a lid on top and allow the broth to come up to a boil, turn the heat down to medium-low and let simmer for about ten minutes, stirring every couple of minutes, until the liquid is thick and saucy.

Top with sliced green onions and serve.