Combine feta and oregano; set aside. Juice the lemon; measure 2 tablespoons lemon juice. Quarter squeezed lemon; set aside. In a mixing bowl stir together lemon juice, olive oil, and pepper. Set aside.
Rinse chicken; pat dry. Starting at the edge of the breast, slip your fingers between the skin and meat, loosening the skin as you work toward the neck end. With your entire hand under the skin, carefully free the skin around the thigh and leg area up to, but not around, the tip of the drumsticks.
Using your hands or a tablespoon, carefully stuff the cheese mixture under skin, filling the drumstick-thigh area first, working up to the breast. Press gently to distribute the feta cheese mixture throughout the space underneath the chicken skin.
Place lemon quarters inside the chicken cavity. Skewer the neck skin to the back; tie the legs to the tail. Twist wings under back. Rub the lemon-oil mixture over entire bird. Place chicken, breast side up, on a rack in a shallow pan. Insert a meat thermometer into the center of an inside thigh muscle. Do not allow thermometer to touch bone.
Roast, uncovered, a 375 degree F oven for 1-1/4 to 1-3/4 hours or until drumsticks move easily and meat is no longer pink and thermometer registers 180 degrees F. Remove chicken from oven. Loosely cover and let stand 10 minutes. Serve with lemon wedges, if desired. Makes 6 servings.