In a medium bowl, whisk together Greek yogurt, buttermilk, dill, lemon juice, lemon zest and garlic; season with salt and pepper, to taste; set aside.
In a small bowl, combine oregano, basil, thyme, paprika, garlic powder, 1 teaspoon salt and ½ teaspoon pepper. Season chicken with oregano mixture.
Preheat grill to medium heat.
Add chicken to grill, and cook, turning occasionally, until chicken is completely cooked through, reaching an internal temperature of 165 degrees F, about 10 minutes.
To assemble the salad, place romaine lettuce in a large bowl; top with chicken, cucumber, tomatoes, avocado, onion, olives and feta. Pour the tzatziki dressing on top of the salad and gently toss to combine.
Serve immediately.
