Heat the oil in a large Dutch oven over medium-high heat.
Season the chicken with salt and pepper. Add chicken to the Dutch oven and brown on each side, about 8 minutes total. Remove to a plate and reserve.
Add sausage, onion, bell pepper, celery, garlic, and thyme and saute until translucent and sausage is browned, about 8 minutes.
Stir in rice, tomato paste, diced tomatoes, broth, bay leaf, and reserved chicken, and bring to a boil, then reduce to a simmer, and cook on low, covered, for 20 minutes.
Turn off heat and let rice stand, covered, 5 minutes. Remove bay leaf. Fluff rice with fork and stir in green onions and parsley.