Heat the olive oil in a large pot or Dutch oven over medium-high heat.
Add the sliced andouille sausage and diced chicken breast, browning the meat until the edges are golden and crisp.
Stir in the diced onion, green bell pepper, and celery, sautéing for 5 minutes until the vegetables begin to soften.
Add the minced garlic, smoked paprika, dried thyme, dried oregano, cayenne pepper, sea salt, and black pepper, stirring for 1 minute until highly fragrant.
Pour in the tomato puree and chicken bone broth, then stir in the dry brown rice.
Bring the mixture to a boil, then immediately reduce the heat to low and cover the pot with a tight-fitting lid.
Simmer for 35 to 40 minutes, or until the rice is tender and the liquid has been fully absorbed.
Remove from heat, let sit covered for 5 minutes, then fluff with a fork and serve.