In a large skillet, heat the olive oil over medium heat. Add the sliced andouille sausage and cook until browned, about 5 minutes. Remove the sausage from the skillet and set aside.
Add the chopped onion, bell peppers, and celery to the same skillet. Sauté for 5-7 minutes, or until the vegetables are softened.
Add the minced garlic to the skillet and cook for 1-2 minutes, until fragrant.
Push the vegetables to the side of the skillet and add the chicken thighs, seasoning them with salt, pepper, paprika, and thyme. Cook for about 6-7 minutes on each side, or until the chicken is browned and cooked through.
Once the chicken is cooked, return the browned sausage to the skillet. Stir everything together and let cook for another 5 minutes to allow flavors to meld.
Taste and adjust seasoning if necessary. If desired, sprinkle with chopped parsley for garnish before serving.