Preheat the grill to high heat. Place the chicken in a baking dish and top with vinegar, oil, herbs, 1/2 teaspoon salt and pepper to taste. Mix to coat and allow the chicken to marinate for at least 15 minutes.
For the Tzatziki Sauce: Cut the cucumber in half. Use half for the tzatziki sauce and slice the remaining half for the salad. Peel the half of the cucumber for the tzatziki sauce and grate it with a cheese grater. Wrap the shredded cucumber in paper towel and squeeze it firmly over the sink to extract extra moisture. Then place the cumber in a bowl. Add the yogurt, zest on 1 lemon, 1 tablespoon lemon juice, olive oil, garlic, dill, salt and pepper. Mix well and refrigerate until ready to serve.
Once the grill is hot, lower the heat to medium and grill the chicken for approximately 5 minutes per side. Remove the chicken and allow it to rest 5 minutes before cutting.
For the Salad: Pile chopped romaine in 4 bowls. Cut the flat bread into wedges. Slice the chicken and layer on top of each salad. Then arrange mint, red onion, cucumbers, tomato, flat bread wedges and tzatziki sauce all around the chicken.
NOTES: For a classic Chicken Gyro Recipe, place 4 warmed flatbreads on plates. Pile each romaine, mint, red onion, cucumbers, tomato and top with chicken and tzatziki sauce.