Combine chicken, lemon zest, lemon juice, oregano, garlic, and salt in a zip-top bag. Marinate for at least 20 minutes or overnight.
Preheat oven to 350°F (180°C).
Remove chicken from marinade, reserving the marinade.
Heat 1/2 tablespoon olive oil in a deep, oven-safe skillet over medium-high heat.
Place chicken skin-side down and cook until golden brown. Flip and brown the other side. Remove and set aside.
Carefully wipe excess fat and browned bits from the pan.
Add remaining 1 tablespoon olive oil to the skillet. Sauté onion until translucent.
Stir in rice, chicken broth, water, oregano, salt, pepper, and reserved marinade.
Bring mixture to a simmer and let simmer for 30 seconds.
Place chicken on top of the rice. Cover with a lid and bake for 35 minutes.
Remove lid and bake an additional 10 minutes, or until rice is tender and liquid is absorbed.
Remove from oven and let rest for 5–10 minutes.
Garnish with chopped herbs and fresh lemon zest before serving.