Preheat the oven to 375 degrees Fahrenheit. Grease an 8x8 or 9x9 baking dish.
Spread the uncooked rice evenly across the bottom of the dish.
Scatter the sliced mushrooms over the rice.
In a medium bowl, whisk together the cream of mushroom soup, chicken broth, and dried thyme. Pour this liquid over the rice and mushrooms.
Place the chicken thighs on top of the mixture. Season the chicken lightly with salt and pepper.
Cover tightly with foil and bake for 40 minutes.
Remove the foil, sprinkle with parmesan cheese, and bake for another 10 minutes until the chicken is cooked through and the rice is tender.