In a large Dutch oven over medium heat, heat the oil.
Add the onion and bell peppers and season with salt and pepper.
Cook until soft, about 5 minutes.
Stir in the chicken and season with salt, pepper, and oregano.
Cook until the chicken is golden, about 5 minutes, then stir in the andouille sausage, garlic, and tomato paste and cook until fragrant, about 1 minute more.
Add chicken broth, crushed tomatoes, rice, and Old Bay.
Reduce heat to medium low, cover with a tight fitting lid, and cook until the rice is tender and the liquid is almost absorbed, about 20 minutes.
Add the shrimp and cook until pink, 3 to 5 minutes.
Stir in green onions just before serving.