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In a large bowl, mix the yogurt, garlic, olive oil, smoked paprika, cumin, onion powder, cayenne, salt, and black pepper into a thick paste.
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Pat the chicken dry with paper towels. Rub the yogurt marinade all over the chicken — under the skin, inside the cavity, everywhere. Place in a large bowl or roasting pan, cover, and refrigerate for at least 4 hours (overnight is best).
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When ready to cook, pull the chicken out of the fridge and let it sit at room temperature for 30-45 minutes. Preheat your oven to 425°F.
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Place the chicken breast-side up on a rack in a roasting pan. Tuck the wings under the body and tie the legs together with kitchen twine if you like.
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Roast for 1 hour and 15 minutes, or until the skin is deeply golden and crispy and a thermometer inserted in the thickest part of the thigh reads 165°F.
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Let the chicken rest for 15 minutes before carving. The yogurt marinade makes this bird incredibly juicy, so don't skip the resting — it needs time to reabsorb all those good juices.