01 - Whisk together olive oil, lemon zest and juice, garlic, oregano, thyme, salt, and pepper in a bowl. Add chicken breasts and turn to coat evenly. Cover and refrigerate for at least 15 minutes, up to 4 hours for deeper flavor.
02 - Preheat oven to 425°F.
03 - Heat a grill pan or skillet over medium-high heat. Cook marinated chicken for 5 to 6 minutes per side until golden brown and cooked through to an internal temperature of 165°F. Let rest for 5 minutes, then slice into thin strips.
04 - Combine Greek yogurt and chopped fresh dill in a small bowl. Mix until well blended and set aside.
05 - Place flatbreads on a baking sheet. Spread an even layer of dill yogurt over each flatbread. Distribute sliced chicken, cherry tomatoes, red onion, olives, and crumbled feta across the surface.
06 - Bake for 8 to 10 minutes until flatbread edges are crispy and toppings are heated through.
07 - Remove from oven. Scatter fresh arugula over the top, drizzle with extra virgin olive oil, and finish with freshly ground black pepper. Slice into wedges and serve immediately.