In a large bowl, combine ground chicken, lemon juice, oregano, basil, olives, green onions, garlic, olive brine, feta cheese and black pepper. Thoroughly mix. Cover with plastic wrap and chill for at least 30 minutes.
Form the mixture into 4 patties. Grill over medium heat for 5 minutes on each side or until a meat thermometer reads 165° and juices run clear. To toast the hamburger buns, place buns face down on the top rack of the grill and toast.
To assemble the chicken burgers, spread tzatziki sauce on top and bottom bun and layer with lettuce, chicken burger, tomato, red onion and pepperocinis.