Preheat the oven to 375 degrees and lightly grease a 9x13 baking dish.
Rinse the wild rice under cold water, then spread it evenly across the bottom of the prepared dish.
Scatter the diced onion, sliced carrots, and diced celery over the rice.
In a bowl, whisk together the cream of chicken soup, chicken broth, dried thyme, salt, and pepper until smooth.
Pour the soup mixture over the vegetables and rice in the dish.
Nestle the chicken thighs into the mixture, pressing them down slightly so they are mostly covered.
Cover the dish tightly with foil and bake for 60 minutes.
Remove the foil, sprinkle the shredded cheddar cheese over the top, and bake uncovered for 15 more minutes until the cheese melts and the rice is tender.