In a large skillet, heat 1 tablespoon of olive oil over medium-high heat.
Sprinkle 1/2 teaspoon of salt over the chicken pieces and cut them into bite-sized chunks. In a skillet, brown them for 4 to 5 minutes over medium-high heat, stirring occasionally. Then, move the chicken to a 6-quart slow cooker.
Slice the sausage thinly and put the pieces in the same skillet. Fry them for 2 minutes, flipping them over once, until they are lightly browned. Move the sausage to the slow cooker.
Cut the garlic, onion, green pepper, jalapeño, and celery into small pieces. Put them in the skillet with the thyme leaves. Add 1 teaspoon of salt and 1/2 teaspoon of pepper. Stir them every few minutes and cook until they are soft, about 5 minutes.
In the slow cooker, put the vegetable mixture, cajun seasoning, chicken broth, and diced tomatoes. Mix everything well.
Put the lid on the slow cooker and set it to low for 4 hours, or until the chicken is soft and easy to cut.
Season the shrimp with salt and cook them in the same skillet over medium-high heat until they turn pink, flipping them once halfway through, for about 6 minutes total. Transfer them to the fridge, and add them back at the end.
Cook the rice according to the package directions and set it aside. Next, transfer the rice to a slow cooker after four hours and simmer it for 15 minutes. Lastly, stir in the shrimp and warm them for five minutes.
Garnish with chopped scallions.
