Season the chicken pieces uniformly with salt, black pepper, and half of the dried oregano.
Heat olive oil in a large deep skillet or Dutch oven over medium-high heat until shimmering.
Add chicken pieces in a single layer and sear until browned on all sides, approximately 5 minutes; remove chicken from the pan and set aside.
Reduce heat to medium, add diced onion to the residual fat, and sauté for 3 minutes until translucent.
Add minced garlic and cook for 60 seconds until fragrant.
Incorporate the rinsed rice and remaining oregano, stirring for 2 minutes to toast the grains and coat them in oil.
Deglaze the pan with chicken broth and lemon juice, using a wooden spoon to scrape the fond from the bottom.
Return the browned chicken to the pan, bring the liquid to a rolling boil, then immediately reduce heat to low.
Cover with a tight-fitting lid and simmer for 15 to 18 minutes until the liquid is fully absorbed and the rice is tender.
Remove from heat and allow the dish to rest, covered, for 5 minutes.
Fluff the rice with a fork, then fold in the lemon zest, fresh parsley, and crumbled feta cheese before serving.