Heat olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
Add sliced andouille sausage and cook until browned, about 5 minutes. Remove sausage with a slotted spoon and set aside.
Add chicken pieces to the pot and cook until browned on all sides, about 6-8 minutes. Remove chicken and set aside with sausage.
Add diced green bell pepper, red bell pepper, onion, and celery to the pot. Cook until vegetables are softened, about 5 minutes.
Stir in minced garlic and cook for 1 minute until fragrant.
Add diced tomatoes with juice, smoked paprika, oregano, thyme, cayenne pepper, black pepper, and salt. Stir to combine.
Pour in chicken broth and bring the mixture to a boil.
Add uncooked penne pasta to the boiling broth. Reduce heat to medium-low and simmer uncovered, stirring occasionally, until pasta is almost tender, about 12 minutes.
Return cooked sausage and chicken to the pot and stir to combine.
Add raw shrimp on top of the pasta mixture, cover the pot, and cook until shrimp turn pink and are cooked through, about 5 minutes.
Remove from heat. Stir in sliced green onions and chopped parsley.
Let the jambalaya rest for 5 minutes before serving.