Preheat oven to 350°. In the bottom of a 3-quart baking dish, combine rice, onion, coconut milk, broth, and 2 tablespoons thyme. Season with 1 ½ teaspoons salt and ½ teaspoon pepper and stir to combine.
Season chicken thighs with ½ teaspoon salt and a large pinch of pepper. Nestle chicken skin side up into rice mixture. Brush exposed chicken with coconut oil and sprinkle with remaining 1 teaspoon thyme.
Cover dish with foil and bake for 1 hour. Uncover and increase oven to broil. Broil until golden, about 10 more minutes.
Garnish with parsley before serving.
