Preheat oven to 450 degrees. Let chicken stand at room temperature for 30 minutes. Rub chicken all over with cut side of garlic. Season cavity with salt and pepper; stuff with garlic halves and thyme. Brush chicken with butter; generously season with salt and pepper. Transfer chicken to a rimmed baking sheet. Cross legs, and tie with kitchen twine.
Roast chicken, basting after 30 minutes, until skin is crisp and golden and an instant-read thermometer inserted into thickest part of thigh reaches 165, about 1 hour. Let stand for 10 minutes before carving. Garnish with thyme.