Coat the inside of a 6-quart slow cooker with cooking spray. Layer the potatoes, olives, if desired, tomatoes, and chickpeas in the cooker; sprinkle with 1/4 teaspoon of the salt. Add chicken pieces to the cooker. Sprinkle with remaining 1/4 teaspoon salt and pepper. Cover and cook on low-heat setting for 7 hours.
Remove the chicken from the slow cooker and set aside. Use a slotted spoon to transfer potatoes, olives, tomatoes, and chickpeas to a platter (discard remaining liquid in cooker). Top vegetables on platter with chicken. Squeeze lemon halves over chicken and vegetables. Sprinkle with parsley.