Marinate the chicken by combining olive oil, lemon juice, oregano, garlic powder, salt, and pepper in a bowl. Add chicken and coat evenly. Cover and refrigerate for at least 30 minutes.

Cook the rice by bringing chicken broth or water to a boil in a saucepan. Add rice, butter or olive oil, and salt. Reduce heat, cover, and simmer for 15-20 minutes. Let sit for 5 minutes before fluffing.

Grill the marinated chicken on medium-high heat for 6-7 minutes on each side until cooked through. Let rest for a few minutes before slicing.

Combine the rice and chicken in a serving dish. Garnish with parsley, feta cheese, and serve with lemon wedges.