Combine chili powder, paprika, sugar, salt, garlic powder and pepper in a small bowl.
Trim any excess fat from the turkey. Using heavy-duty kitchen shears or poultry shears, cut the turkey down one side of the backbone, through the ribs. Make an identical cut on the opposite side to remove the backbone completely; discard or reserve for turkey broth. Place the turkey, cut-side down, on a cutting board and flatten with the heel of your hand (you'll have to press hard!). Splay the thighs outward and tuck the wings under. Loosen the skin over the breasts and thighs; rub the spice mixture under the skin.
Light a chimney starter full of charcoal. When all charcoal is lit, pour the coals to one side of the grill and let it burn down to medium heat (about 400 degrees F). Wearing an oven mitt, carefully place a foil or foil-lined drip pan under the grill rack on the unheated side (see Tip). Place the turkey, breast-side up, on the rack over the pan.
Continue cooking, rotating the bird so the side furthest from the heat is now closest to the heat (not flipping) and adding more coals halfway through, until an instant-read thermometer inserted into the thickest part of the breast and thigh registers 165 degrees F, 2 to 2 1/2 hours. Remove from the grill and let rest for 20 minutes before carving.