Heat oil in a large pot. Cook chicken and sausage until browned. Remove and set aside.
Sauté onion, bell pepper, and celery until softened. Add garlic and cook until fragrant.
Stir in rice, toast slightly. Add paprika, cayenne pepper, thyme, bay leaves, salt, and pepper.
Return chicken and sausage to the pot. Pour in chicken stock and bring to a boil.
Reduce heat, cover, and simmer for 20-25 minutes until rice is tender.
Fold in shrimp during the last 5 minutes of cooking. Cook until shrimp are pink and opaque.
Remove from heat, discard bay leaves, and let sit covered for 5 minutes.
Garnish with green onions and parsley. Serve with crusty French bread.