Toss the chicken with 1 tablespoon olive oil, oregano, garlic powder, 1/4 teaspoon salt, and pepper.
Warm the remaining olive oil in a large skillet over medium-high heat. Cook the chicken for 8 to 10 minutes, turning occasionally, until browned and cooked through.
Combine the rice, broth, lemon zest, lemon juice, and the remaining salt in a saucepan. Bring to a boil, cover, reduce the heat, and simmer for 18 minutes. Rest covered for 5 minutes, then fluff.
Divide the lemon rice among four bowls. Add the chicken, cucumber, tomatoes, feta, yogurt, and parsley.
Finish each bowl with a squeeze of lemon and serve warm.