Preheat grill to medium. Pour vinegar into a large bowl. Slowly whisk in oil until incorporated and thickened. Whisk in oregano, garlic, 1/2 teaspoon salt and 1/8 teaspoon of pepper.
Coat chicken with cooking spray; sprinkle with remaining 1/2 teaspoon salt and 1/8 teaspoon pepper. Grill until browned on both sides and juices run clear (155ºF internal temperature), 5 to 6 minutes per side.
Immediately transfer hot grilled chicken to a bowl and toss to coat in the vinegar mixture. Let cool for 5 minutes. Slice chicken on a slight diagonal and return to the bowl to coat. Remove coated chicken to a plate.
Add lettuce, cucumber, tomatoes, onion, olives, and feta to the bowl with the vinegar mixture and toss to coat. Remove the salad to a platter or plates. Arrange the sliced chicken over the top and serve with lemon wedges for squeezing.
Tip: For a grilled garnish, grilled the lemon wedges cut-side down until they’re nicely browned, 1 to 2 minutes per side. Serve with the salad and squeeze over it.