Preheat the oven to 350°F (175°C).
In a large skillet, heat olive oil over medium heat. Add chopped onion and cook for 3-4 minutes until softened.
Add minced garlic to the skillet and cook for 1 minute until fragrant.
Add the chicken pieces to the skillet and cook for 5-6 minutes until lightly browned but not fully cooked through. Remove from heat.
In a large mixing bowl, combine uncooked rice, chicken broth, cream of mushroom soup, sour cream, shredded cheddar cheese, dried thyme, salt, and black pepper. Stir until well combined.
Add the cooked onion, garlic, and chicken pieces to the rice mixture and stir to combine evenly.
Transfer the mixture to a greased 9×13 inch casserole dish and spread evenly.
Cover the casserole dish tightly with aluminum foil and bake in the preheated oven for 40 minutes.
While the casserole is baking, bring a large pot of salted water to a boil. Add trimmed green beans and cook for 4-5 minutes until tender-crisp.
Drain the green beans and return them to the pot. Add butter, salt, and black pepper. Toss to coat and keep warm.
After 40 minutes, remove the casserole from the oven and carefully remove the foil.
Bake uncovered for an additional 5 minutes to allow the cheese on top to melt and slightly brown.
Remove the casserole from the oven and let it rest for 5 minutes before serving.
Serve the chicken rice casserole hot with the buttered green beans on the side.