In a mixing bowl, whisk together olive oil, lemon juice, minced garlic, oregano, thyme, salt, and pepper. Marinate chicken for 30 minutes to 2 hours.

In another bowl, combine Greek yogurt, grated cucumber, minced garlic, olive oil, lemon juice, dill, and parsley. Mix until smooth and chill for 30 minutes.

Preheat grill to medium-high heat. Remove chicken from marinade, grill for 6-7 minutes per side, until cooked through. Let it rest for 5 minutes before slicing.

On a platter, arrange a bed of romaine lettuce, add sliced cucumbers, olives, and red onion.

Top salad with sliced chicken and drizzle with tzatziki. Garnish with fresh parsley and serve with warm pita bread.