In a large pot or Dutch oven, heat the olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté for about 5 minutes until the vegetables are softened and the onion is translucent. Stir in the minced garlic and dried thyme, cooking for an additional minute until fragrant.
Add the diced chicken breasts to the pot. Season with salt and pepper, stirring to combine. Cook for about 5-7 minutes until the chicken is no longer pink and lightly browned.
Stir in the long-grain white rice, ensuring it is well-coated with the mixture. Pour in the chicken broth, bringing the mixture to a gentle boil. Reduce the heat to low, cover, and let the soup simmer for about 15-20 minutes, or until the rice is tender.
Once the rice is cooked, stir in the shredded cheddar cheese until melted and creamy. Pour in the milk, stirring until everything is well combined. Let the soup heat through for an additional 5 minutes.
Ladle the Cheesy Chicken and Rice Soup into bowls, garnishing with additional cheese or fresh herbs if desired. Enjoy this comforting bowl of goodness, paired with crusty bread or a light salad.