Preheat the oven to 375°F and lightly grease a 9x13 baking dish.
In a medium saucepan, combine the wild rice and chicken broth. Bring to a boil, then reduce heat, cover, and simmer for 40 minutes until the rice is tender and most of the liquid is absorbed.
While the rice cooks, heat a large skillet over medium heat. Add the chicken pieces and cook until lightly browned on all sides, about 5 minutes.
Add the onion, carrots, and celery to the skillet with the chicken. Cook for another 5 minutes until the vegetables begin to soften.
Stir in the heavy cream, dried thyme, salt, and black pepper. Simmer for 2 minutes to let the flavors blend.
Remove the skillet from heat and fold in the cooked wild rice until everything is evenly combined.
Transfer the mixture to the prepared baking dish and sprinkle the shredded cheddar cheese evenly over the top.
Bake uncovered for 20 minutes until the cheese is melted and the edges are bubbling. Let it rest for 5 minutes before serving.