Immerse planks in water, placing a weight on top of each plank to keep it submerged. Soak at least 4 hours or overnight.
Meanwhile, mix dressing, 1/4 cup of the parsley, the lemon zest and juice until well blended.
Remove 1/4 cup of the dressing mixture; set aside for later use.
Pour remaining dressing mixture into large resealable plastic bag; add chicken. Seal bag; turn over several times to evenly coat chicken with the dressing mixture. Refrigerate at least 2 hours.
Preheat grill to medium heat.
Remove planks from water; brush tops with oil.
Remove chicken from marinade; discard bag and marinade.
Place 2 chicken breasts on each plank.
Place on grate of grill; cover with lid.
Grill 1 to 1-1/4 hours or until chicken is cooked through (165F). Meanwhile, mix reserved dressing mixture, remaining 1/4 cup parsley and the olives.
Remove chicken from grill; discard planks.
Remove bones from chicken; cut each breast in half.