Place the rice in a bowl and cover with water. Soak for 10 to 15 minutes, then drain.
While the rice is soaking, saute the vegetables. To do so, add the olive oil to a large skillet, along with the onion, carrots, and celery. Saute over medium-high heat, stirring occasionally, until vegetables have softened, but are still al dente, about 8 minutes. Add the garlic, all the seasonings, and salt and saute another 2 minutes.
Transfer the rice, sauteed vegetables, broth, and wine to a large (6-quart) crock pot. Add the raw chopped chicken and stir.
Cover the crock pot and place on the lowest setting. Cook 4 to 6 hours, or until chicken is cooked through, rice is puffy, and vegetables have softened. Taste soup for flavor and add salt as desired.
Serve heaping bowls with gluten-free crackers or bread.