In a large stockpot or dutch oven over medium-high heat 1 tablespoon of the olive oil, once hot, add the andouille sausage rounds and chicken, saute until nicely browned, about 5 - 8 minutes. Transfer to a paper towel-lined plate.

Add the remaining olive oil to the dutch oven and add the peppers, celery, onions, and garlic. Saute until onions are softened, about 5 minutes.

Add the diced tomatoes, chicken stock, Creole seasoning, bay leaves, and potatoes. Bring to a boil, then reduce to a simmer, and cook until potatoes are tender, about 20 - 30 minutes, stirring occasionally.

Add the sausage and chicken back in and stir to mix in well, then add in the shrimp and continue to simmer until the shrimp have cooked through and are pink, about 5 - 7 minutes.

Remove bay leaves, season to taste, and garnish with diced green onions if desired.