1. Prepare grill for indirect grilling. If using a gas grill, heat one side to medium-high and leave one side with no heat. If using a charcoal grill, arrange hot coals on either side of charcoal grate, leaving an empty space in middle.
2. Combine first 7 ingredients; set aside.
3. Remove and discard giblets and neck from chicken. Trim excess fat. Place chicken, breast side down, on a cutting surface. Cut chicken in half lengthwise along backbone, cutting to, but not through, other side. Turn chicken over. Starting at neck cavity, loosen skin from breast and drumsticks by inserting fingers, gently pushing between skin and meat. Rub spice mixture under skin. Gently press skin to secure.
4. Place chicken, breast side down, on grill rack coated with cooking spray over direct heat; cover and cook 7 minutes. Turn chicken over; cook 7 minutes. Move chicken over indirect heat; cover and cook 45 minutes or until a thermometer inserted in meaty part of thigh registers 165°. Transfer chicken to a cutting board; let rest 10 minutes. Discard skin.
Wine note: An economical meal can include wine. With Grilled Spice-Rubbed Whole Chicken, look to Australia. The Little Penguin Chardonnay 2008 ($6) has juicy stone fruit and mango flavors that couple nicely with the chicken's sweet meat, while a touch of toasty oak helps it to integrate with smoky grilled flavors and eclectic spices. —Jeffery Lindenmuth