In resealable freezer bag, combine chicken, olive oil, dill, lemon zest, garlic, chili flakes, salt and pepper; mix well. Seal and refrigerate for at least 30 minutes or up to 4 hours.
Prepare rice according to package directions. Set aside.
Preheat grill to medium-high. Remove chicken from marinade; grill for 5 to 7 minutes per side or until chicken is cooked through and instant-read thermometer inserted in center reads 165°F.
Serve chicken over bed of rice; top with cucumber, tomatoes, cheese and olives. Drizzle with tzatziki and sprinkle with parsley.
Substitute chicken breasts for thighs if desired.