In a bowl, add the Greek yogurt, olive oil, cucumbers, dill, garlic, vinegar, lemon juice, salt, and white pepper and stir until well combined. Set aside until ready to serve.
Heat the olive oil in a large skillet set over medium heat. Add the chicken, cumin, paprika, garlic powder, cayenne pepper, salt, and pepper. Heat until the chicken is well coated and just warmed through, 3 to 4 minutes.
Divide the brown rice among four serving bowls. Top with the chicken, olives, tomatoes, red onions, lettuce, and feta cheese.
