Cook the Meats
Heat olive oil in a large pot or Dutch oven over medium-high heat. Add diced chicken and cook until browned (about 4–5 minutes). Remove and set aside. Add sausage to the pot and sear until lightly browned, then remove.
Sauté the Veggies
In the same pot, sauté onion, bell pepper, and celery for 4–5 minutes until softened. Add garlic and cook another 30 seconds.
Add Seasonings and Rice
Stir in paprika, thyme, cayenne, black pepper, and salt. Add rice and cook for 1 minute, stirring to coat the grains in flavor.
Simmer the Jambalaya
Return chicken and sausage to the pot. Pour in diced tomatoes with their juices and chicken broth. Stir well, bring to a boil, then reduce heat to low. Cover and simmer for 20 minutes.
Add Shrimp and Finish
Stir in shrimp and cover again. Cook for another 5–7 minutes, or until shrimp are pink and rice is fully cooked.
Serve
Fluff with a fork, garnish with green onions and parsley, and serve hot.