Dice the chicken breast into bite-sized pieces and slice the andouille sausage into thin rounds.
Heat the olive oil in a large heavy-bottomed pot or Dutch oven over medium heat.
Add the chicken and sausage to the pot and sauté until browned on all sides, then remove the meat and set it aside on a plate.
In the same pot, add the diced onion, bell pepper, and celery, sautéing for 5 to 7 minutes until the vegetables are soft and translucent.
Stir in the minced garlic, Creole seasoning, dried thyme, sea salt, and black pepper, cooking for 1 minute until highly aromatic.
Add the dry white rice to the pot and stir for 1 to 2 minutes to lightly toast the grains.
Pour in the tomato puree and chicken bone broth, using a wooden spoon to scrape up any browned bits from the bottom of the pot.
Return the chicken and sausage to the pot and bring the mixture to a gentle boil.
Reduce the heat to low, cover with a tight-fitting lid, and simmer for 18 to 20 minutes until the rice is tender and the liquid is fully absorbed.
Remove from heat and let the jambalaya sit covered for 5 minutes before fluffing with a fork and garnishing with freshly chopped parsley.