Season the chicken well with salt, pepper and half of the oregano. Heat the oil in a pot or 12-inch skillet over medium-high heat until lightly smoking. Add the chicken, skin-side down and cook until well browned, 6 to 10 minutes, flip and then brown the other side, 3 to 4 minutes more. Remove to a plate and set aside.
Discard all but 1 tablespoon fat from skillet and heat the fat over medium heat until shimmering. Add the onion and a pinch of salt and cook, stirring, until softened, about 3 minutes. Add the remaining oregano and garlic and cook until fragrant, about 30 seconds.
Add the rice, stirring until fragrant and lightly toasted, about 1 minute, then add the stock and artichoke hearts and stir together. Nestle the chicken thighs on top, skin-side up, adjust the heat to maintain a simmer. Cover and cook until the chicken and rice are done 15 to 20 minutes more. Sprinkle with lemon zest, lemon juice and feta. Serve immediately.