1. Remove and discard giblets and neck from chicken. Cut the chicken into drumsticks, thighs, and breasts; cut each breast in half crosswise to form 4 breast pieces total. Reserve wings and back for another use.
2. Combine rind and next 7 ingredients (through garlic) in a small bowl, and stir with a whisk. Place juice mixture in a large zip-top plastic bag. Add chicken to bag; seal and marinate in refrigerator 1 hour. Remove chicken from bag, and discard marinade. Sprinkle chicken evenly with salt.
3. Prepare grill to medium-high heat. After preheating, turn the left burner off (leave the right burner on), or arrange charcoal on one side of grill for indirect heat.
4. Place chicken on grill rack covering right burner; grill over direct heat 15 minutes, turning every 5 minutes. Move chicken to grill rack covering left burner; grill over indirect heat 10 minutes or until a thermometer registers 165°. Discard chicken skin.