Remove backbone from chicken using kitchen shears.
Combine mayonnaise and next 4 ingredients in a large heavy-duty zip-top plastic bag; add chicken. Seal and turn to coat. Marinate in refrigerator 8 hours, turning bag occasionally.
Remove chicken from marinade, and discard marinade.
Heat a large cast-iron skillet over medium-high heat. Coat pan with cooking spray.
Add chicken to pan.
Place 2 bricks wrapped in heavy-duty foil over chicken, pressing down to flatten. Cook 20 minutes; turn chicken over. Reposition bricks. Cook an additional 20 minutes or until chicken is done.
Remove skin from chicken, and cut into quarters. Carve chicken.