Heat a large pan with a lid over medium-high heat. Add enough vegetable oil to coat the bottom. Cook the chicken and sausage for 6-8 minutes, stirring occasionally, until browned and fully cooked. Remove from the pan and set aside.
Add more oil to the pan if needed, then sauté the bell peppers, onion, garlic, and celery for 5-7 minutes until softened.
Pour in the chicken stock, crushed tomatoes, thyme, cayenne pepper, and Cajun seasoning. Stir everything together and bring to a boil.
Add the rice, reduce the heat to low, and simmer for 20 minutes, stirring occasionally to prevent sticking or burning.
Add the frozen shrimp and cook for another 4-6 minutes, stirring occasionally. Return the cooked chicken and sausage to the pan.
Once the jambalaya thickens, taste and adjust the seasoning with more Cajun seasoning, salt, or pepper if needed.
Serve hot, garnished with green onions.