Preheat the oven to 375°F (190°C).
In a large skillet, heat olive oil over medium heat. Add the chopped onion and minced garlic and sauté until softened, about 3-4 minutes.
Add the chicken pieces to the skillet and cook until they are no longer pink on the outside, about 5 minutes. Remove from heat.
In a large mixing bowl, combine the uncooked rice, chicken broth, cream of mushroom soup, sour cream, dried thyme, salt, and black pepper. Stir well to combine.
Add the cooked chicken, sautéed onions and garlic, and frozen peas to the rice mixture. Stir until everything is evenly distributed.
Transfer the mixture to a greased 9×13 inch baking dish and spread it out evenly.
Cover the baking dish tightly with aluminum foil and bake in the preheated oven for 40 minutes.
Remove the foil and sprinkle the shredded cheddar cheese evenly over the casserole.
Return the casserole to the oven, uncovered, and bake 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.