Heat olive oil in a large pot or Dutch oven over medium-high heat.
Add diced chicken and sliced andouille sausage to the pot. Cook until the chicken is no longer pink and the sausage is browned, about 6-8 minutes. Transfer the cooked chicken and sausage to a plate and set aside.
In the same pot, add diced onion, bell peppers, celery, and minced garlic. Cook until the vegetables are softened, about 5-6 minutes.
Stir in the uncooked rice, crushed tomatoes, chicken stock, Cajun seasoning, dried thyme, dried oregano, paprika, and cayenne pepper (if using). Season with salt and black pepper to taste.
Return the cooked chicken and sausage to the pot. Stir everything together until well combined.
Bring the mixture to a simmer, then reduce the heat to low. Cover and let it cook until the rice is tender and most of the liquid is absorbed, about 20-25 minutes, stirring occasionally.
Once the rice is cooked, remove the pot from heat. Let it sit, covered, for about 5 minutes to allow the flavors to meld together.
Taste and adjust seasoning if needed. Serve hot, garnished with chopped green onions, fresh parsley, and hot sauce if desired. Enjoy your delicious jambalaya!