Heat the olive oil in a large skillet over medium heat. Add the chicken pieces, season with salt, pepper, and oregano, and cook until lightly browned on all sides, about 5 minutes.
Add the diced onion and cook for 3 minutes until it softens. Stir in the garlic and cook for 30 seconds more.
Add the rice to the skillet and stir to coat it with the oil and juices. Pour in the chicken broth, lemon zest, and lemon juice. Bring the mixture to a boil.
Reduce the heat to low, cover the skillet, and simmer for 15 minutes until the rice is tender and most of the liquid has been absorbed.
Remove the lid and gently stir in the olives. Sprinkle the feta and parsley over the top. Cover again and let it sit off the heat for 3 minutes so the feta softens slightly.