Thaw the hen if frozen. Rinse, remove the giblets and neck, and pat dry. Make several slits in the skin, then split the hen in half along the breastbone. Mix together 1/3 teaspoon of the chili powder, salt, pepper, and lime juice. Rub the mixture all over the poultry and set aside for about 15 minutes.
In a blender, puree the yogurt, garlic, ginger, onion, cumin, turmeric, and the remaining chili powder. Place the poultry pieces in a bowl and add the yogurt mixture. Mix well to coat all the pieces. Cover and refrigerate for at least 8 hours, turning occasionally.
Preheat the oven to 400 degrees F. Place the hen, skin side up, on a rack in a roasting pan. Spoon the yogurt mixture over it from time to time until thoroughly cooked, 45 to 60 minutes or until the hen is very tender. Test for doneness by pricking the skin of the thigh; the juice should run clear. Serve hot.
Remove the skin before eating, and garnish with lime and cilantro or parsley, if using.