Make marinade: In a small bowl, whisk together lemon zest and juice, oregano, oil, 2 teaspoons coarse salt, and 1 teaspoon pepper. Divide marinade between 2 large resealable plastic bags. Place 2 chicken halves in each bag; shake to coat. Let marinate at room temperature 30 minutes, turning bags occasionally.
Preheat grill to medium; lightly oil grates. Remove chicken from marinade, and pat dry with paper towels. Place chicken, skin side up, on grill. Cover and cook, until lightly browned and cooked through, about 20 minutes. Turn chicken over; cover and cook until well browned, 10 to 15 minutes (an instant-read thermometer should register 175 degrees.when inserted into thickest part of meat, avoiding bone). If chicken is browning too quickly, move to cooler parts of grill or turn grill to low heat.
Transfer chicken to a cutting board. Tent with foil; let rest 10 minutes. Meanwhile, place lemon halves on grill, cut side down; cook until slightly charred, 8 to 10 minutes. Cut chicken pieces in half; serve with grilled lemon halves, and, if desired, garnish with oregano sprigs.