Marinate. Toss the chicken with the zest, lemon juice, 1 tablespoon oregano, garlic, 1/2 teaspoon salt, and 1/2 tablespoon oil in a bag and chill at least 20 minutes. Sear. Brown the chicken skin side down in 1 tablespoon hot oil for 5 to 7 minutes, flip for 2 minutes, and set aside.
Soften the onion. Cook the onion in the pot for 2 to 3 minutes, then add the reserved garlic for 30 seconds.
Coat the rice. Stir the rice into the fat for 1 minute.
Add liquid. Pour in the broth, water, leftover marinade, remaining oregano, 3/4 teaspoon salt, and pepper, scraping the pot, and bring to a simmer.
Cook. Place the chicken skin side up on the rice, cover, and cook on low for 25 minutes until the chicken is 175 degrees F near the bone.
Rest. Rest covered 5 to 10 minutes, loosen the rice, and top with lemon zest and parsley.