Preheat the oven to 350°F (175°C).
In a large skillet, heat olive oil over medium heat. Add the chopped onion and sauté for 3-4 minutes until translucent.
Add the minced garlic and chicken pieces to the skillet. Cook for 5-7 minutes until the chicken is no longer pink, stirring occasionally.
In a large mixing bowl, combine the uncooked rice, chicken broth, cream of mushroom soup, sour cream, shredded cheddar cheese, dried thyme, salt, and black pepper. Mix well.
Add the cooked chicken, onions, and garlic mixture to the rice mixture and stir to combine.
Pour the mixture into a greased 9×13 inch casserole dish and spread evenly.
Arrange the trimmed fresh green beans on top of the casserole mixture.
Cover the casserole dish tightly with aluminum foil and bake in the preheated oven for 40 minutes.
Remove the foil and sprinkle shredded mozzarella cheese evenly over the green beans.
Return the casserole to the oven and bake uncovered for an additional 5 minutes, or until the cheese is melted and bubbly.
Remove from oven and let it rest for 5 minutes before serving.