Heat the oven to 400 °F. Pat the chicken thighs dry and season all over with the oregano, garlic powder, salt and pepper.
Heat 1 tbsp of the olive oil in a large oven-safe skillet over medium-high. Sear the chicken skin-side down until deep golden, 6-7 minutes, then flip and cook 2 minutes more. Move the chicken to a plate; it finishes in the oven.
Add the remaining 1 tbsp oil and the garlic to the skillet and cook 30 seconds. Stir in the rice and lemon zest, pour in the broth, and scrape up the browned bits. Simmer 1 minute.
Nestle the chicken skin-side up into the rice. Cover the skillet with a lid or foil and bake 20 minutes.
Uncover, scatter the green beans around the chicken with a pinch of salt, and bake until the rice is tender and the chicken reads 165 °F in the thickest part, 12-15 minutes.
Squeeze the lemon juice over the skillet, let it rest 5 minutes, then fluff the rice and serve.