Add butter to the drippings and melt. Add onion and cook, stirring often, until translucent, about 3 minutes. Add garlic; cook for 1 minute. Add rice; cook, stirring to coat grains in drippings and lightly toast, about 1 minute. Stir in 3 cups stock and remaining salt and pepper. Bring to a boil. Use a wooden spoon to scrape any browned bits from the bottom of the Dutch oven. Place the chicken thighs over the rice.