Heat the olive oil in a large pot over medium heat and brown the chicken (about 2-3 minutes). Remove chicken and set aside.
Add the sausage and brown on both sides (about 2-3 minutes). Remove and set aside.
Add the onions and green pepper and cook until softened, about 2 minutes.
Add the tomatoes, Cajun seasoning and thyme and stir to combine.
Add the chicken stock, rice, chicken and sausage and stir to combine.
Bring to a boil, reduce heat and simmer, covered, for 15 minutes.
Remove the lid and let simmer the last 5-10 minutes uncovered so any additional liquid can be absorbed. *If it gets too dry, put the lid back on to finish the cooking.
Remove from heat, fluff with a fork and serve garnished with green onions.
Notes
If the rice gets too dry while cooking for the last 5-10 minutes, just put the lid back on to let it finish cooking.
For more heat, add ¼ to ½ teaspoon cayenne pepper or some diced hot peppers.
Make sure the rice is rinsed until the water runs clear to prevent the rice from getting sticky while cooking.
Substitute any smoked sausage for the andouille if needed.