1- Heat olive oil in a grill pan or skillet over medium-high heat. Season the chicken breasts with dried oregano, salt, and pepper. Grill the chicken for 5-7 minutes on each side until fully cooked and internal temperature reaches 165°F (74°C). Let it rest for a few minutes, then slice into strips.
2- In a large bowl, combine the romaine lettuce, cherry tomatoes, red onion, cucumber slices, and Kalamata olives. Drizzle the Greek salad dressing over the top and toss to coat all the ingredients evenly.
3- Place the grilled chicken strips over the tossed salad. Spoon dollops of the chilled tzatziki over the salad and chicken. Sprinkle crumbled feta cheese and some extra chopped fresh dill over the salad.