In a medium bowl, combine olive oil, lemon juice, minced garlic, dried oregano, dried thyme, and salt and pepper to taste. Add chicken breasts, ensuring they are coated. Cover and refrigerate for at least 30 minutes.

In a small bowl, whisk together Greek yogurt, grated cucumber, minced garlic, olive oil, lemon juice, dill, parsley, and a pinch of salt. Stir until smooth and refrigerate.

Preheat grill to medium-high heat. Remove chicken from marinade and grill for 6-7 minutes on each side or until internal temperature reaches 165°F. Let rest for 5 minutes before slicing.

In a large salad bowl, create a base with chopped romaine lettuce. Layer with sliced cucumbers, red onions, and Kalamata olives. Top with grilled chicken pieces.

Spoon tzatziki sauce generously over chicken and garnish with parsley. Serve immediately with pita bread or lemon wedges.